From Dragon Ball Encyclopedia, the ''Dragon Ball'' wiki
Several characters in Dragon Ball have tails (尻尾), or tails (シッポ, Shippo) that, depending on the character, can be used for several different things.
All Saiyans have a monkey-like tail that allows them to transform into a Great Ape when they look at a full moon. When it 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. Most of the Saiyans in the anime get their tails removed, but on some occasions, they grow back. Full blooded Saiyans such as Raditz or Nappa wrapped their tails around their waist in a belt like fashion, likely to keep it from being gripped easily by an opponent.
After blowing up the moon to stop Son Gohan's transformation, 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 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' attack.
In DBZ Episode 1, Raditz whips Krillin in the face with his tail. In DBZ Episode 3, 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.
During the battle with the Saiyans, Piccolo devises a plan that involves him grabbing Nappa's tail. This plan fails, however, as Nappa is immune to this weakness.
Broly clearly has a tail during the flashback to his infancy, but as an adult he does not appear to have a tail. It is most likely that Paragus either removed it to prevent the already-insane and powerful Broly from transforming into a Great Ape at the full moon, or that Broly was wearing the tail in a similar fashion to a belt (similar to most tailed saiyans encountered barring Goku and Gohan), and it was unseen due to Broly's red clothing covering it. In the movie [[Dragon Ball Z: Bio-Broly], Broly's clone has a tail before he is transformed into Bio-Broly.
Bardock is one of the only Saiyans (Other than the actual residents of Planet Vegeta) to keep his tail until his death. He usually wears it around his waist in a belt-like fashion. He uses it to transform into a Great Ape at the beginning of Bardock: The Father of Goku. It is incinerated along with the rest of his body by Frieza.
The Planet Elite Forcehad 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.
In battle, Freeza 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, but when he turns into his fourth form, his tail is completely intact, though part of it is destroyed when he is hit with Goku's Spirit Bomb. Freeza also has the uncanny ability to grow his tail longer in battle.
Future 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 Androids 17 and 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 canon (excluding Dragon Ball GT, if one can count it), the "tail" theme seems to diminish after Cell achieves perfection.
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 ocarina is broken, and Hirudegarn stomps on Hoy, Trunks cuts off Hirudegarn's tail with Tapion's sword. Trunks is about to kill Hirudegarn when Goku stops him, and kills the monster himself with the Dragon Fist.