From Dragon Ball Encyclopedia, the ''Dragon Ball'' wiki
Self-Destruction (自爆, Jibaku; Literally meaning "Destruct") is simply the act of releasing all of one's energy in an explosive, suicidal blast. It is a last ditch effort used only when a fighter is not strong enough to defeat their opponent by any other means. Users of this attack often attempt to grab their opponent first in order to maximize the damage. Despite its lethal powers, there has only been one successful Self-Destruction attack in the entire series.
The Saibaiman fighting against Yamucha killed him in the first and only successful Self-Destruction in the series (this version was called Saibaiman Bomb in the Budokai Tenkaichi video game series). Chaozu used it himself shortly after against Nappa to little effect (this version was called Farewell, Mr. Tien). Many of Dr. Gero's creations had an explosive installed to simulate this effect, though No. 16 was the only one who attempted to use it (this version was called Self-Destruct Device). Semi-Perfect Cell used it as well in an attempt to destroy Earth (this version was called Unforgivable! in Dragon Ball Z: Budokai Tenkaichi 3).
Vegeta used a technique that was similar against Boo named the Saishyuu Saigo no Waza, or Ultimate Final Skill. This was called Final Explosion in the English translations of the Budokai video game series. This variant was different in that it created a huge 360 degree expanding golden energy burst of Ki in the shape of a large dome around the user, but did not cause the user's body to explode. Vegeta's body turned to stone and crumbled into dust afterwards though.
 Android Bomb
Android Bombs were self-destruct devices implanted in the chest areas of all four known Artificial Humans created by Dr. Gero. These devices could be triggered either by the Androids themselves or via a remote control.
Artificial Human No. 16, Artificial Human No. 17, and Artificial Human No. 18 were known to have had implanted explosive devices, while Cell also demonstrated an ability to self-destruct at will. In the Dragon Ball anime filler, Artificial Human No. 8 was the first to be shown to have an implanted explosive device.
These bombs were used for various purposes. They were originally intended to keep control of the Androids, ensuring that they could easily be destroyed if they turned against their creator. Android 16 demonstrated an attempt to trigger his own self-destruct device in order to destroy Perfect Cell, but Bulma Brief had already removed his bomb and his attempt failed. Cell also attempted to self destruct, however, he used a special technique to do so, rather than a simple explosive device. The strength of the bombs were said by Bulma to be equal to that of an atomic bomb in the dub.
 Final Explosion
Vegeta had a variation of the self destruct ability where he gathers all of his energy into and around himself, causing his aura to sparkle. When he releases it all, it causes an atomic explosion several to many times stronger than any other self destruct attack that uses up absolutely all his energy along with his lifeforce. The result of his type of explosion leaves behind a lifeless shell in his image that crumbles into dust, but the explosion itself makes a crater nearly a mile wide. He turned into stone because of the fact that he used what energy kept him alive. Vegeta does not actually name this attack, but it is commonly referred to as such by several video games. In Dragon Ball GT, Son Goku attempted to use the same move to finish off Omega Shenron but stopped under Vegeta's prompting. He also attempted to use a variation of it to finish off Super 17, but the super Android's barrier kept them both alive.
 Revenge Death Bomber
Super Boo's base form had a suicide attack that also caused a giant explosion, though it is colored pink. Even though Buu is much stronger than Vegeta, the explosion is not as large or powerful since Buu was not willing to kill himself in the attack, instead using it as an outward blast like the Hyper Exploding Demon Wave (or Super Explosive Wave). The attack still hurt him, though, so it most likely counts as a self destruct. Like Final Explosion, this attack was named by the Budokai Tenkaichi video game series.
 Goodbye, Mr. Tien
This was the self-destruct attack Chaozu used against Nappa during the Saiyan Saga. Even through he used the technique, Nappa did not even get hurt. In Dragon Ball Z: Budokai Tenkaichi 3 and Dragon Ball: Raging Blast, it is Chaozu's Ultimate Blast. At the end of the attack (when Chaozu exploded), Tenshinhan yelled, "Chiaotzu!!!".
 Non-manga usage
While sparring against Piccolo in the Other World, Chaozu grabbed onto Piccolo's back and began to partly initiate the Jibaku, but before he could complete it Piccolo plucked him off and slammed him into the ground.
When Vegeta told the story of the Super Saiyan legend, the similar move was used by the Original Super Saiyan who could not control his power due to it being so high, so he self destructed (although the filler scene at the end shows his power blowing up the planet that he was on rather than showing him blow up.)
In Dragon Ball GT, Goku uses this technique against Super 17 but is saved from destruction when the artificial human puts up a forcefield that somehow shields both himself and Goku from the blast. Goku also comes close to using this technique against Omega Shenron, but Vegeta's arrival distracts Goku allowing Omega Shenron to escape Goku's grasp. This prompts Goku to cancel the technique.