This page lists all the fusion characters plus all the other "combinations" characters have formed thoughout the series.
Definitions
Fusion Dance - This is when two people do a funky dance and then the two become fused together, stronger than ever. This fusion only lasts for 30 minutes and can not be done again for about 60 minutes. Although, it is worth the wait! Supposedly if the fused character use a lot of energy, the fusion time is reduced, however, unlikely. Also, if the characters fuse while SSJ or another form, the fused character will also be in another form. If the fusion partners make a mistake performing the dance, the fusion will either not work at all, or the fused character will be a wacky form that is weaker than each character.
Potara Earrings - Each partner puts an earring on opposite ears, the two will be drawn to each other and will form the fusion character. These earrings allow the partners to fuse forever unless they fuse with a magical being. Also, it is believed if one breaks one of the earrings, they will un-fuse, otherwise it's permanent. However, the effects of the fusion earrings do not function correctly while inside a magical being and will cause the character to un-fuse. This fusion does not make any mistakes and is rather quick, unlike the Fusion Dance. Considered to produce a weaker fusion character (yet still stronger than both of the partners combined) than the one that would yeild from the fusion dance.
Combination - A type of "fusion" without using the two above methods.
Fused Characters
Gojita = Gokou + Vejita + Dance
SSJ4 Gojita = SSJ4 Gokou + SSJ4 Vejita + Dance
Gotenks = Goten + Trunks + Dance
SSJ & SSJ3 Gotenks = SSJ Goten + SSJ Trunks + Dance
Kaiobit = Kaio-shin + Kibbit + Potara
Rou Dai Kaio-shin = Rou Dai Kaio-shin + Some Magician + Potara
Vegitto = Vejita + Gokou + Potara
And you cannot forget the fusion of Gokou and Mr. Satan (potara). This fusion never happened, however, Gokou needed a fusion partner (before Vejita showed up) to beat Majin Buu and only Mr. Satan was around. This character was what Gokou thought him and Mr. Satan would become. He's funny looking ^_^
Also, Toriyama had another gag fusion which never occurred, it was just a "what if" kinda thing in the back of one of the mangas. Pirrin = Piccolo + Kuririn + Dance. Now this fused character is weird looking.
Other Fusions/Combinations
Note: Piccolo split into two Piccolo's: one good (which became Kame-sama), one evil (which became Piccolo Daimao who spawned Ma Junior)
Piccolo = Ma Junior (the one we all know and love) + Kame-sama
Super Juusangou (Super 13) = Juusangou (13) plus the CPU's of the late Juushigou (13) & Juugogou (14)
Super Juunanagou (Super 17) = Juunanagou (in the real world) + Juunanagou (constructed in Hell)