Counter-Strike and Team Fortress started out as mods and later became very popular. I think Team Fortress started on the Unreal Engine, then became TFC on the Half-Life engine (which I think stemmed from a Quake engine) and is now coming as Team Fortress 2 on the Source engine in Half-Life 2: Orange Box.
Some mods can almost feel like a full game rather than a mod. Take the Source Engine mod, Insurgency for example. The Insurgency Mod, while lacking some polish and general balance, is a complete Source Engine conversion and they created just about everything in it from scratch. Another Source mod, Black Mesa, is a mod being made to completly remake the Half-Life experience on the Source Engine and that is going to be a complete conversion as well as they're making just about everything from scratch. A little history on that, Valve released Half-Life: Source, which turned out to essentially be Half-Life 1.5 with some Source Engine effects and some polished graphics, but that was it (and the reason the Black Mesa mod is being made).