The only games I've never gotten around to finishing are:

Splinter Cell- They just get too hard near the end. Double Agent is the only one I could finish, and incidentally the worst in the series

God of War- I really want to finish this. I got GoW II when I was about 3/4 of the way through, though. Then I got my PS3 and neglected it and now my PS2 refuses to run it.

B/C in a firmware update, Sony, PLEASE!

Oh also Shadow of the Colossus. I got bored after the sixth one.

hehe..I have the same exact problem. I'm currently in the process trading in games I no longer play or have any interest in. Why keep games and you might never play them. I just have a problem when every time I walk in a game store I walk out with about 5 or 6 used games that were cheap. I just can not walk past a deal on some games. But what I have to realize is that "will I finish those 5 or 6 games?". That's what stops me and thats what I'm doing now. I'm cleaning my whole library out, so its just 1 or 2 games I will play per console (PS3, 360, Wii, DS, PSP, PS2, Xbox, Gamecube) once that happens I'm good, and I can play those 1 or 2 games until I beat them.

Keeping one or two games in your inventory per console helps out a lot. So try it. By having 2 games per console. You shouldn't buy two of the same games within the same genre. You should try to buy two different games in two different genres. That would help.

The thing I am going to try now, is to buy 1 GC game and 1PS2 game and I am playing a PS1 game now, so then I have three games, and I won´t buy any more games before I am finished with those three games (if i make that :P)
The games I am planning to buy is:

GC: Viewtiful Joe
PS: Vagrant Story (already have and started playing it)
PS2: I have no idea, any ideas?

@sennaho

Good plan, you more than likely have the same plan I'm doing now.

Gamecube-wise thats a nice selection. I was going to get Viewtiful Joe or probably some other game I can't think of from the top of my head.

PS1- good choice I think, I never heard of that game before.

PS2- well whatever you like bra. I mean if shooters are your thing, try some GTA or Metal Gear Solid.