My list would be:

1. GTA: San Andreas (PS2)
2. Kingdom Hearts (PS2)
3. Mario Galaxy (Wii)
4. MGS4 (PS3)
5. Crackdown (360)

i always play the games that i own till i finish them, even if the gen is over.
as for the games that i do not own , thanfully i do not have any this gen all the games i missed out on i got =]

Hmmm... usually I estimate all games I own lol BUT Killzone 2. I really wanna play the Online again, but I borrowed it to a friend of mine like 5 months ago so... >_>

Oh and Fat Princess! I forgot it lol Played the story (well actually my cousin did, I was busy on the laptop at that time) no online, nothing. Got one trophy tho :P

1. MGS 4
2. Bioshock
3. Assassin's Creed
4. Prince of Persia trilogy on PS2
5. Splinter Cell trilogy on PS2

Gears 1,2 - only played 10 mins and got bored
Halo 3, ODST - 20mins of each, got bored
Mass Effect - put about 8 hours in and got fed up with the jerky gameplay, good game though
UFC - played against friends loads, not touched campaign
Tekken 6 - got it on Xbox, not keen on controls
Ratchet & Clank: Tools of destruction - not even put it in my drive
MAG - got fed up of dying so thinking of selling it, only level 3
Assassins Creed 2, Borderlands, Prototype, Darksiders, Prince of Persia, GTA 4, Midnight Club LA

Oops you said 5. I keep buying games in sales or off friends 2nd hand and never playing them, too scared to miss a bargain. :(

Fatal Frame 1-3
Dark Cloud 2
Yakuza
Shinobi
Skygunner

All of those are PS2 games. I've played a bit of all of them, enjoyed the little that I played, but for some reason or another, I just haven't gotten around to delving deeper into them and finishing them. I actually have like 80+ PS2 games that I haven't gotten around to playing yet (and probably never will :-/), but the five I listed are the ones that I really want to finish at some point.

Not to cast stones at glass houses but you gotta play Bioshock.  It was a great game.

If only I had the time nowadays to finish them.  I finish most of my games but sometimes you just can't keep up and a few games go by the whey side.  If I ever get layed off, I'll get around to them.

i don't too , thats why i said even if the gen is over i take my time.

I would love to play Gears again, I gave up on the first Berserker as I got pretty bored at the time, wish I had given it another go now.

Mass Effect series - still haven't played those yet :/

Fable Lost Chapters - my favourite game of all time, some pikey stole my copy out of my locker :| Cheap douche.

Metro 2033 - Chances are a friend might let me borrow it.

Borderlands - Seems like the sort of game I would enjoy, but never seem to have enough cash to buy it and when I do I tend to buy games higher on my priority list that tend to be more expensive