Tonberries first appeared in FFV, like you said. They were very annoying and powerful enemies in the Underwater Tunnel (Name I can't remember.)
They appeared in FFVI again, dubbed "Pug" in FFIIIe. They were normal enemies, and "Master Pug" (Master Tonberry) was a boss in a treasure chest in the Ancient Castle.
In FFVII, They were enemies in the Northern Crater. (Master Tonberries.) You can Morph them into Ribbons! *drools*..
In FFVIII, monsters again. They appeared in the Centra Ruins (Name?) After killing (actually defeating, not carding, my friend carded like 30 not knowing that
) about 20 of them, the Tonberry King appears. After you defeat him, you obtain him as a GF, and he has many useful "Shop" abilities, especially useful in the Time Compressed World.
In FFIX, They appeared in Ipsen's Castle. (Other places? I don't remember.) They gave very little Exp, and often appeared in groups. Run. Use "Flee". What are you waiting for, run dammit!!!
In FFX, they were enemies in the Cavern of the Stolen Fayth (Yojimbo's place.), Master Tonberries appeared in the Omega Ruins, and I think there was one more species...Also, "Don Tonberry" in the Monster Arena is the key to maxing out your characters' Sphere Levels.