In Universe 7, Saiyans are born with a monkey-like tail that allows them to transform into a Great Ape when they look at a full moon. Saiyans who lived on Planet Vegeta, like Bardock, Paragus, King Vegeta, Vegeta, Nappa, and Raditz, wear their tail wrapped around their waist in a belt like fashion. This custom is likely to keep their tails from being reached and gripped easily by opponents. When a Saiyan's tail is squeezed, it causes them agonizing pain, though Nappa and Vegeta become immune to this. Goku also became immune to this weakness, shown when Krillin attempted to squeeze his tail, to no avail. If a Saiyan's tail is cut off while they are in Great Ape form, they revert to normal.
In Dragon Ball Minus, Gine and Bardock are shown letting their tails hang loose while at home on Planet Vegeta, indicating that Saiyans only wrap them around their waist when invading planets or when in battle, but let them hang loose when at home on Planet Vegeta and/or off duty.
Many of the Saiyans in the anime get their tails removed, but on some occasions, they grow back. The Daizenshuu description is that the tail will often suddenly grow back if the Saiyan is in danger; such as when it did during Goku's match against Giran or for Gohan during the battle against Vegeta.
Goku uses the Super Saiyan transformation while at the same time possessing a tail in Dragon Ball GT, but sometimes his tail does not change color to gold. The fur is still brown when Bardock turns Super Saiyan in Dragon Ball: Episode of Bardock. However, when Goku turns Super Saiyan 3, his tail fur always turns gold. When Goku and Vegeta turn Super Saiyan 4. Their tail furs both take the color of their respective Super Saiyan 4 fur.
Saiyans native to Universe 6, do not possess tails due to the evolution process they underwent in their universe as explained by Cabba in the manga, though in the anime, Cabba has never heard nor has knowledge of Saiyan tails.
Saiyan tails can burn easily when exposed to fire.
Bardock usually wears his tail around his waist in a belt-like fashion. He uses it to transform into a Great Ape at the beginning of Dragon Ball Z: Bardock - The Father of Goku, and he still has it when sent back in time in Dragon Ball: Episode of Bardock. The Masked Saiyan/Xeno Bardock also has a tail in Dragon Ball Online, Dragon Ball Heroes, and Dragon Ball Xenoverse 2.
In Dragon Ball Minus, Bardock is shown letting his tail hang loose while on Planet Vegeta with his wife Gine.
In Dragon Ball Minus, Gine wears her tail loose though this is likely due to her having retired from the Saiyan Army and working in a non-combat role as a meat processing employee on Planet Vegeta.
Bardock's Planet Elite Force
Bardock's Planet Elite Force had tails, and wore them in the same way Bardock did. They used them to transform into Great Apes along with Bardock at the beginning of Bardock - The Father of Goku. Bardock's Crew are all killed by Dodoria and his elite soldiers.
Goku burned his tail as he is flying over the burning Fire Mountain. Goku loses his tail three times: the first time was when Puar transformed into a pair of scissors, and cuts it off after Goku transformed into a Great Ape in Pilaf's Castle. It ends up growing back during his fight with Giran at the 21st World Martial Arts Tournament. Later, Grandpa Gohan grabbed Goku's (still weak and untrained) tail during a fight at Fortuneteller Baba's Palace and accidentally pulled it off. Then, his tail grows back in between the time after the defeat of Terror and Plague, and before the defeat of Sky Dragon by Goku. During the 22nd World Martial Arts Tournament, Goku is shown to have heeded the advice of his grandfather, as he is no longer weakened by having his tail grabbed as demonstrated when Krillin attempts to weaken Goku by grabbing his tail during their match. Lastly, Goku's tail was permanently removed by Kami at the end of Dragon Ball, but it was regrown by Old Kai's tail pulling technique in Dragon Ball GT to increase his power and grant Goku access to the Golden Great Ape and Super Saiyan 4 transformations. Yet, the tail is not seen at the end of the GT series when Goku is an adult again.
After blowing up the moon to stop Gohan's rampage as a Great Ape, Piccolo yanked Gohan's tail off. In the anime only, the tail grew back, but was once again removed by Piccolo. It grew back for the second (third, counting the anime-only instance of his regrowing his tail) and final time during the battle with Vegeta, and to stop his transformation, Vegeta cut off his tail with an energy disk, and it has not grown back since, though it has been featured in the movies Dragon Ball Z: The Tree of Might and Cooler's Revenge. In The Tree of Might it is cut off by Goku to end his transformation and, by doing so, protecting him from Turles' Kill Driver. In Cooler's Revenge, Gohan tail is shown to have apparently grown back at some point after Goku's return to Earth. Interestingly, Gohan's tail allows Cooler's Armored Squadron to identify as one of the surviving Saiyans, causing them to briefly mistake him for the Saiyan they were searching for, unaware that Gohan was the son of the Saiyan who had defeated Frieza. Gohan's tail proved to be a liability during his initial encounter with Cooler's henchman, as Dore managed to grab him by the tail, weakening the young half-saiyan and preventing him from fighting back. Fortunately Dore chose to simply toy with Gohan rather than kill him, playfully swing the boy around by his tail. Gohan was later saved by the arrival of his father Goku. As the movie is one of the few films without any real problems (save for a few minor inconsistences) fitting within the series timeline (as it seemingly occurs during the three-year wait for the Androids) it is possible Gohan's tail was likely removed following the events due to the liability it posed both as a weakness and the threat posed by Gohan's Great Ape form.
In the second episode of Dragon Ball Z, Raditz whips Krillin in the face with his tail. In the next episode, Goku squeezes Raditz's tail, causing him terrible agony and getting him down for Piccolo to use another Special Beam Cannon, but Raditz tricks Goku into letting him go. When placing Raditz in a Full-Nelson, Goku explains he did not grab his brother's tail once again because he feared that Raditz would most likely sever his own tail to escape if he tried to (Raditz's own response implies that he would have severed his tail had Goku tried to grab it a second time). All of these events occur in the manga as well.
In Dragon Ball Xenoverse 2, Nappa states that Raditz would always skip tail training, thus explaining why he was susceptible to being weakened when his tail was pulled unlike his partners Nappa and Vegeta who had trained to overcome it.
During the battle with the Saiyans, Piccolo devises a plan that involves him grabbing Nappa's tail. However, this plan fails, as Nappa is immune to this weakness and beats Piccolo, Gohan, and Krillin. In Xenoverse 2, Nappa mentions training his tail.
Vegeta's tail is cut off by Yajirobe and does not grow back. Though in Dragon Ball GT, it is regrown twice through artificial means. The first time is when Vegeta is under the control of Baby, and it is cut off by Goku. The second time is when it is regrown again so that he can become a Super Saiyan 4, but he does not retain this tail after he returns to his base form.
The movie villain Broly is shown to have a tail, as seen in flashback to his infancy. As an adult, his tail is not seen, but in a concept arts of Broly shows that his tail is hidden under his clothing. In Dragon Ball Z: Bio-Broly, it is shown that Broly's clone has a tail as an adult before he is transformed into Bio-Broly. The original Broly is implied to have retained his tail in Dragon Ball Heroes due to his accessing the Super Saiyan 4 form, which requires both that he have a tail, and become a Great Ape and control his actions in that form. In the Legendary Super Saiyan Saga of Dragon Ball Xenoverse, Bardock destroys the Power Ball (created by Vegeta) that he used to transform, in order to prevent Dark Broly from transforming into his Great Ape form.
Tarble seems to be the last living Saiyan to be seen still having his original tail. When he arrives on Earth to request Vegeta's help, his tail quickly gives away his Saiyan heritage. Unlike most Saiyans, Tarble does not wrap his tail around his waist in a belt like fashion.
The monster from the Muscle Tower, Buyon, can attack his opponents with his long and powerful tail. He uses this against Goku and Android 8. He also uses this attack as a boss in the video game Dragon Ball: Origins 2.
The Pirate Robot has a tail that he can electrify to attack and shock his opponent. The robot usually wraps its tail around its opponent before sending the surge of electricity through it. The robot uses this attack against Goku, after dragging him underwater. The Pirate Robot can also use this attack in Dragon Ball: Advanced Adventure and Dragon Ball: Origins 2.
The Frieza Race is shown to have extendible tails, as evidenced by Frieza in his second form extending his tail in a feint attack on Gohan, Krillin, Vegeta, and Dende shortly after transforming, as well as Chilled using his tail to attack Ipana. In Dragon Ball Online it is shown that the tissue making their race's tails can give a potent power boost to those who eat it, as after taking a bite out of the part of second form Frieza's tail that was cut off by Krillin, the Time Breaker Frieza Soldier who ate that part of Frieza's tail mutated, becoming larger and much stronger. Their tails ability to mutate individuals that eat them is a unique attribute to Frieza's race.
In battle, Frieza uses his tail mainly to slap enemies or strangle them. He does this to Vegeta and later Goku, though Goku bites him. When he is in his second form, it is cut off by Krillin with a Destructo Disk (causing him to threaten to eat Krillin) though he seemed to partially regrow his tail shortly before he transformed into his Third form. When he turns into his fourth form, his tail is restored, though part of it is destroyed again when he is hit with Goku's Spirit Bomb. After being rebuilt as Mecha Frieza, his tail was replaced with a cybernetic one. After being resurrected by the Dragon Balls, Frieza completely regenerates a new tail after the pieces of his body are placed in the Frieza Force's more advanced Medical Machine.
Cooler also sports a tail. Upon hearing of his brother's death while on a conquered planet, he is shown swatting away the remains of a throne behind him with his tail. During his fight with Goku, he attempts to whip his tail at Goku while fighting him underwater, before firing a Ki Blast at Goku.
In Dragon Ball Super, Frost uses his tail while fighting during the Tournament of Destroyers. While on the run in Universe 6 after his deception of the public is revealed by Cabba, Frost is shown to have modified his tail to secrete his Secret Poison.
Future Warrior (Xenoverse 2)
In Dragon Ball Xenoverse 2, the Frieza Race Future Warrior has a tail and can use the Tail Attack as their grab throw. If the Mecha Frieza Suit is worn, their tail will take on the appearance of Mecha Frieza's artificial tail.
Cell's tail is perhaps the deadliest of them all; he uses it to absorb people. He usually absorbs them by jabbing them with the stinger on his tail and then sucking them in, one bit at a time. This is a painful procedure that kills the victim being absorbed. When absorbing androids, however, the stinger on his tail opens up to suck the android in and swallow them whole. Cell does this to Android 17 and Android 18 in order to transform. In his perfect form, the tail retracts, though he does open it up again to spit out seven Cell Juniors. In Dragon Ball GT, he also extends it to absorb Goku in the same manner as 17 and 18, though he escapes.
In manga and anime, the "tail" theme seems to diminish after Cell achieves perfection. Due to his Namekian cells, Cell can also regenerate his tail if it is cut off.
Android 21 (Good/Evil)
In her true form, Android 21 has a tail similar Frieza's in his final form though with the same pink skin as Majin Buu presumably due to her Majin cells being dominant. Like Frieza, she can extend her tail which she utilizes by thrusting her tail into the ground and having it erupt from the ground to attack her opponent.
In Dragon Ball Z: Wrath of the Dragon, Hirudegarn's tail serves the same purpose as Cell's; he eats people with it, except he is much larger than Cell, and when his tail opens up, cords extend from it that wrap around victims and suck them in. After Tapion's Hero's Flute is broken, and Hirudegarn stomps on Hoi, Trunks cuts off Hirudegarn's tail with Tapion's Brave Sword. Trunks attempts to attack again Hirudegarn when Goku stops him, and kills the monster himself with Dragon Fist.
Like his brother, Champa also possesses a tail, however it is shorter than Beerus. Given that Champa has never been seen using the Tail Attack, it is possible that its size prevents him from using his tail to attack.
Video Game Appearances
In Dragon Ball Xenoverse, the Saiyan Tail appears when certain Battle Armors worn by Saiyans are equipped such as Battle Suit (Vegeta, On entry), Battle Suit (Raditz), Battle Suit (Nappa), Battle Suit (Bardock), and Battle Suit (Turles). Additionally the Gold Battle Suit and Crystal Battle Suit have tails that are the same metallic color as the suit itself. These saiyan tails appear when the suit is worn regardless of race and thus do not represent a Saiyan Future Warrior's actual tail. Combining these Battle Suit pieces with certain clothing options together may result in the tail not appearing at all. Additionally a Great Ape's tail serves as a weak point which can be grabbed when a Great Ape's guard is down, allowing the fighter to pick up the Great Ape by the tail and slam them into the ground to cause a decent amount of damage. However Great Apes can also use a tail attack to attack behind them and unless their in a guard down state they will resist having their tail pulled by throwing the one attempting to grab their tail off. Frieza Race Time Patrollers can use their tail to attack during certain combos and their grab throw.
In Dragon Ball Xenoverse 2, in addition to the Saiyan Battle Suits that have saiyan tails from Xenoverse, Battle Suit (King Vegeta) and Battle Suit (Fasha) also feature Saiyans tails wrapped around the waist when worn regardless of race. Additionally the tails of Great Apes still function as a weak point in Xenoverse 2. Frieza Race members can use their tails to perform tail attacks as part of their combos or grab throw. As part of the Super Pack 1 DLC, Frost's tail is used as part of his own unique version of the tail attack where he uses it to grab an opponent's leg as he passes by them, then kicks them from behind while holding on to their leg before letting go as they are knocked away by his kick.
"A tail modeled after the tails of the Saiyan warrior race that called Planet Vegeta home."
— Dragon Ball Xenoverse 2 Saiyan Tail accessory description
In Xenoverse 2 after the 1.07.00 Update, the Saiyan Tail appears as an accessory for the Future Warrior which can be obtained by purchasing it from the TP Medal Shop. The tails description reveals that it is a faux Saiyan Tail modeled after tails of the Saiyans of Universe 7 and can be equipped by all races and genders. This tail also does not change color when a Super Saiyan transformation is used. Interestingly, if worn with Battle Suits (or the lower body portion of Spike the Devil Man Suit which gives the wearer a Devil tail) that give the wearer a Tail wrapped around their waist will appear even when worn with the Saiyan Tail accessory resulting in two tails appearing. The tail will also disappear when the Super Saiyan 3 Awoken Skill is being used.
"A hat and Great Ape tail modeled after a Saiyan who has absorbed over 17 million zenos of Blutz Waves from a powerful light source."
— Dragon Ball Xenoverse 2 Great Ape Hat & Tail accessory description
There is also another accessory called Great Ape Hat & Tail which features a Great Ape style Saiyan Tail along with a hat that resembles a Great Ape's head. Like the Saiyan Tail accessory this tail is also a faux tail designed to resemble a Great Ape's tail and can be equipped by all races and genders.
"A wig and tail modelled after Goku when he powered up beyond Super Saiyan 3 to Super Saiyan 4."
— Dragon Ball Xenoverse 2 Great Ape Hat & Tail accessory description
There is also another accessory called SS4 Wig & Tail (Goku) which is a Super Saiyan 4 Wig and Tail based on Goku's Super Saiyan 4 form.