Freelancer is one of them, but at the time of writing I was actually thinking of Puzzle Quest Galactix (or whatever it was called). The mechanics were awful, but the plot was worse. WAY worse. And it was somewhat unbalanced.
Elite and Starflight annoy me in their own ways. Starflight...I don't know if I would call that nonlinear or not. I mean, what it all comes down to is getting a doohickey from a place, doing a thing to another thing, getting another doohickey and then using that doohickey on something else. But then, Fallout is the same way, Myst is a major canonical example, and Morrowind has like a seven minute speedrun, doesn't it?
Oh right...TBT. Um, Protostar (Starflight 3) was -kinda- like that, though it was more RPGey.
I actually don't find nonlinear games to be very replayable. Doom I can play over and over, on harder modes sometimes, seeing if I can beat it just running through sometimes, killing everything I see and getting everything sometimes. Many options! Fallout though, I dunno, I start it up and I think "Okay, I'm going to do the first few things in order, then I'm going to go here, get this armor, go here and use this broken skill to get great guns, then do these quests and win." All that is thought out before even starting! I might as well not play at all because I already know how it's going to go. Oh this time I'll see what the evil quests are like...okay, that's one other playthrough. Oh this time I'll try and beat it with minimal quests at all, just wilderness stuff. Is that actually fun? Who seriously says "I know! I'll play Fallout 2 again, and this time I'll use method number FOUR to get my vault citizenship in vault city!"