Using the 7th and 6th gen as a reference (these are the only gens where this became a problem) and looking at my collection (100% hands on accurate for those two gens), heres the list of games that I need to finish or at least start (and some of them suck so I'll NEVER play them again):

Xbox 360

Ace Combat 6 (never even tried it)

Assassins Creed 2 (never tried it)

Bee Movie (was pretty fun until I got distracted)

BioShock (Day one purchase. Didn't really like it but I know its a good game)

Blue Dragon (was enjoying it until I got distracted)

Bully (a ton of fun -all my daughter plays!  I only play it when she's stuck.)

Call of Duty 2 (came free with my 1st 360)

Condemened: Criminal Origins (really liked this game.  Just quit playing it one day)

Condemned: 2 (I DID see the title screen --over a year after I bought it!)

Dark Sector: (fun for $7!  I need to go back to it someday)

Dead or Alive Xtreme 2:  (I was horny and it was $9)

Earth Defense Force 2017 (I keep going back to this game but I doubt if I'm halfway through)

Enchanted Arms (never made it to the first battle.  Characters are sooooooooooooo annoying)

Fight Night Round 3 (got it for free from a friend. if I need 1000 quick Achievement Points, I'll play it)

Ghostbusters (Loved this game.  Why did I stop playing it?)

Golden Axe (got distracted.  Forgot I had this one. Good game.)

Grand Theft Auto 4/Episodes (got bored with GTA4/Never got past the title screen in Episodes)

The Orange Box (Only finished Portal.  The best game that I haven't played)

Hitman Contracts (saw a funny youtube video of it and decided to buy it)

Infinite Undiscovery (really liked this game. quit because I didn't want to walk all the way back to the beginning of the game for some quest)

Kung Fu Panda (Came with my 2nd 360.  Was fun.  Quit for no reason)

Lost Planet (Shitty game.  Honestly can't wait for part 2!  What's wrong with me?)

Mass Effect 2 (Victim of FF13's arrival)

NBA Street Home Court (bought it with 9 other games.  This game lost out)

Ninja Gaiden II ($5 game that I intend to play someday)

Onechanbara (surprisingly fun/frustrating game)

Rumble Roses XX (shit game)

Silent Hill Homecoming (great game --victim of too many games in 2010)

Table Tennis (never even tried to play it)

Tenchu Z (the worst $5 I've ever spent.  Shitty game)

Top Spin 2 (loaned it out when I got it. never really played it when I got it back)

XBLA

Aegis Wing (free game)

Commanders Attack (a poor man's Advance Wars)

Hexic HD (free game --was fun)

Marvel vs. Capcom 2 (wanted this game so badly!  But since I'd played the Dreamcast version to death.......)

Spyglass Board Games (nobody to play Chess/Checkers with)

The Maw (Amazing game!  But since my kid beat it, I didn't really feel compelled to play it)

Playstation 3

Dead Space (great game that really needs my attention)

Devil May Cry 4 (is shit, compared to Bayonetta.  Wish I'd played this one first.  I may never play it, now.)

inFamous (started off great but then got incredibly boring.  I want to see the surprise ending, though.)

PSN

Grandia (will get some playtime, VERY soon)

Ragdoll Kung Fu (free game.  I hate the art style.)

PSP

Rainbow Six: Vegas (bought it with my PSP but I didn't have a memory card.  Bought MGSPO with my card and NEVER even tried R6:V)

Wii

Battalion Wars (bought with 9 other games --never even tried it)

Obsure: Aftermath (shit game)

Tony Hawk's Downhill Jam (bought with 9 other games)

Wii Ware / Virtual Console

Art Style: Orbient (gave it as a gift to someone on VGChartz and bought it for myself, too!  Never played it)

Paper Mario (too many current gen games demanded my attention)

Super Punchout!! (was fun until I got the new Punchout!! for the Wii)

Pokemon Puzzle League (I know it's a great game but I just never have the time to play it)

Teenage Mutant Ninja Turtles (beat this on the Nes as a kid.  Damn, it sucked!  I forgot how frustrating this game is!!)

This post is already too long so I'll leave out the DS, Gamecube, Dreamcast, and PS2

Gears! Never really understood how to play it properly

1. Killzone 2 (finished single player once but left a lot of trophies on the table)
2. Bioshock (finished once but left a lot of trophies on the table)
3. Assassin's Creed (did not finish because I lost interest)
4. Motorstorm (did not finish because I lost interest)
5. Tiger Woods 08 (did not finish because I lost interest)

I only have 3, but its a big 3!

God of War 3 (been to busy with FF XIII so far)
Metal Gear Solid 3 (just never got into it much)
Final Fantasy XII (haven't found the time...)

I have Fire Emblem and it looks pretty involving.  I just can't spare the time anymore.

I should've made it a list of 20 games people bought but never really played, now that I think about it.  This thread has only highlighted a lot of what I haven't sompleted :/

ICO was a very unexpectedly amazing game.  It's something you should play. 

Conker's I played when it was the N64, it was alright but halfway through it wasn't amusing anymore but I finished it.  I didn't mind the potty humour but it just got tiring after a while.

GOW2, I have but haven't played through.  It's the only reason why I haven't bought GOW3

I have Metroid Prime 2 and I haven't even played it yet even though I thoroughly enjoyed the first Metroid on the GC. I just can't get myself for playing games on the Wii for some reason.  I guess motion control isn't really for me.

Condemned 2: Bloodshot - 360 - Got bored, looked too dark and ugly, made me nauseous.
Half-Life 2 - XBOX - Also made me nauseus, got to the helicopter, couldn't beat it.
Just Cause - 360 - Repetetive missions, buggy as hell, flying over the island is fun though.
Max Payne 2: The Fall of Max Payne - XBOX - Liked the first one, but for some reason not this.
Sega Superstars Tennis - 360 - Ramdom tasks in adventure mode had nothing to do with tennis. No sense of completion, tasks just kept coming.

Not saying all of these are good games, just saying I could have gotten more out of them if I had toughed it out longer.

Metroid Prime 1 and 2.. and i still haven't brought it yet :(.. i played prime 3 thats because i was just getting back into the game considering i haven't played an Metroid game since Super Metroid

Infamous only half way
Zelda Twilight Princess only 2 hours in
Folklore said my fiancee could beat it first she hasnt played it in 9 months
Valkyria Chronicles only a hour in
Madworld only 2 hours played

If my list was bigger, I'd also add Zelda twilight princess and windwaker.