I enjoy Flip Out and probably play it at least once a year. I've never played it through to completion because it's the type of game I enjoy playing 20 minutes and stopping. Obviously the game is not very pleasant to look at, but I still enjoy the puzzle aspect. I was considering trying to beat it for the first time for this thread, but I guess you beat me to it.
I have the Jaguar GameDrive, so I can play any Jag game, but I don't know of any other games I could play through to completion. Most of the games I enjoy, I'm not great at. I love Power Drive Rally, but I can't finish some of the later more challenging races. I also enjoy Trevor McFur, but I can only beat it with cheat codes. Tempest 2000 is fun, but when I play it, I only play until I run out of lives. I can't beat that game, and I don't enjoy it enough to play it over and over until I get good enough to beat it. Doom is a possibility, but playing it with the Jag controller isn't ideal.