Gogeta:This is the fusion between Goku and Vegeta. We see Gogeta in DBZ Movie #12: The Rebirth of Fusion!! Goku and Vegeta and again at the end of Dragonball GT when Vegeta and Goku are trying to stop Omega Shenron.
Gotenks:The fusion result of Goten and Trunks. Gotenks is seen in the Buu Saga when all else has failed to stop the evil Buu. It takes Goten and Trunks awhile to finally get the fusion right and when they do get it right they mess around to much and end up running through their time limit.
Kamicollo:
This is the fusion between Piccolo and Kami. Since they were once a single being, rejoining the 2 halves made them much stronger than if one of them fused with someone else. Before the 2 fused they decided on keeping Piccolo's body since it was much stronger & younger. This fusion resulted in a powerful Super Namek and was the strongest being on the planet at the time of the fusion.
Kibito Kai:This fusion wasn't intended and happened accidentally when Supreme Kai and Kibito were showing Goku the Potara Earrings.
Old Kai:This fusion happened when an old witch grabbed the Potara Earring off of the Supreme Kai 15 generations back. When the witch put on the earring the two were stuck together forever.
Super 17:When Dr. Gero and Dr. Myuu meat up in hell they make a new Android 17. When this new Android 17 escapes from hell he meets up with the old Android 17 that Gero had made years back. The two fuse and create the all powerful Super 17.
Vegito:We see Vegito when Goku and Vegeta fuse using the Potara Earrings. They would never have fused knowing that they could never again separate but they knew they had to in order to defeat Majin Buu. When Buu absorbed Vegito they happened to defuse. Vegeta and Goku then crushed the Potara Earrings.