There is already a facepalm but a patrick stewart version would have to be epic, just to live up to the meme

WIN
+1

Hmmm, never played? Rather I' ve tried some games for few minutes and threw them away. Some even multiple times, because I often convince myself that the game isn't so bad and give it a shot again. And usually it ends the same way. :-)
But one reason I don't have games I never played is that "luckily" I don't have money to buy games for reserve.
Never threw away game for addiction fear reason, though my cousin does so with Football Manager series. He is able to spend thousands hours with this game so he is trying not ot play it anymore. Once he came three hours later on a date because he couldn't take a break.

When thinking about it, most of those games I've not finished are actually either bought here, or on certain Steam collection packages that has been on sale.
EDIT:
However, most games have been tried at least once, though presumably not for a lengthy period of time.
Here's my Steam account on the so-called steamcalculator.com. The value is not accurate, as there are certain packages it hasn't recognized properly, and most of the games have been bought on sale.

20 from GOG and a about 5 or six from Steam I'm saving for later. Some of those I've played the demo at least. Also I've got a 614k (or something like that) connection, so downloading a new game takes a while and it's not on a whim decision. Also my hard disk is not that big, so I try to keep a limited supply of unfinished games going. I've got about five of those but I've noticed I'm not as dedicated as I used to be. I play a game for about an hour and once I reach some kind of important point I'll save and play something else or leave the comp all together. I used to blaze through a campaign but nowadays if I get killed a couple of times, I get frustrated and quit to try again much later.

There are still some good communties on CSS at least; I don't play 1.6 anymore because I can't find any good gun game servers.
Most servers I play on, the bratty 13 year olds get made fun of. ;)

Lemme think...
I've got:
1 CD copy of Beyond Good and Evil which I haven't played because it wasn't designed to be compatible with my graphics card (at least, I think that's the reason why it's not working...)
3 Steam X-com games that I bought for their classic value, and swiftly decided not to play after getting slaughtered repeatedly over the course of two hours of UFO Defense.
2 CD Copies of Condemned: Criminal Origins that don't work because my computer apparently can't read the disks. Either of them. And neither can any other PC in my house.
1 Copy of The Path that I bought on steam during an indie game sale and haven't played because it sounds a tad creepy and also lags a lot.
1 copy of Gish that I bought during the same indie sale and haven't played because side-scrolling platformers are something I generally suck at.

Way too many. Mostly due to lack of time. I'll get to them someday though. There's just so many games out there! :-)

Now why would you do such a thing? Buy something with your precious money and not even touch it.
WHY?! I like unwrapped games damnit!

In the past year there have been many excellent sales. We all know about Steam and GoG having great sales. There have also been many lots of great sales in various brick & mortar stores that are trying to clear out their PS2, Xbox, and GameCube inventories. I have bought a ton of PS2 games for ridiculously cheap prices. There is a pawn shop chain here in Seattle that sells them for $2 a piece. I have also bought a lot of GameCube games. My backlog has gotten out of hand, but it's hard to pass up when I know that if I don't buy them at the super low price, I may never get another chance to play those games. So I pick them up and add them to the pile. It's just that my rate of buying has been greater than my rate of playing lately. I think I enjoy bargain hunting as much as I enjoy the games themselves.

Nice link, thanks. Funny. I can see what PS's saying. That's why I never really got into MMOs. They'd just decimate my life.
LOL, lots of backlog - going back as far as Dark Wizard for the Sega CD and Bahamut Lagoon for the SNES. I still need to play Lunar. Everyone always tells me how great it is, but I keep putting it off because I never have time. I've more or less given up on RPGs. I love them, but I never have the time anymore.
My PC backlog is equally absurd. Goes back to Gabriel Knight II, which I never really got into because I didn't play the first one (which GOG reminded me of - and I subsequently purchased). Blood.net is another one that I've been meaning to play forever. Ditto Shivers II.
The big one for me is Xenosaga II. I really like the story, but it's not as good as XSI. Also the gameplay is fairly bad. Still, I really want to play XSIII, which I've heard is absolutely fantastic.
I have to agree with jungletoad, if you collect games, you tend to get rare or odd ones that you want to play when you see them at the right price or before they go out of print, not when you're ready to play them. A backlog is inevitable.
Oh Prator, play Condemned. Sooooo good if you like horror games. One of my favorites of recent years. I played it in XB360 though, no clue on whether the PC differs meaningfully.

Never started at all, not played for longer than a couple of minutes, or never finished?
1st: 8 games, all from GOG
2nd: uh... many more?
3rd: almost all the games I have

Slowly beginning to make my way through the backlog, but it so far consists of :
-Europa Universalis Rome : Gold Edition
-Europa Universalis 3 : Heir to the Throne
-East India Company
-Majesty 2
-King's Bounty : Armored Princess
-Freedom Force pack
-Birth of America 2 : Wars in America
-AI War : Fleet Command
-Sword of the Stars
-Crown of Glory : Emperor's Edition
-Men of War
-Tropico 3
-Commandos 2&3 pack
-Evil Genius

I know most of this already. I still have four serious problems with the game:
1. There's no obvious plot, besides what's described in the manual, and none of your legions of identical mooks have any real personality.
2. The game is EXTREMELY unforgiving. The manual only gives you the most basic instructions. Failing to do ALL of the things you listed in your post may result in a game-over eventually. Also, none of the combat situation buttons are labeled for some reason.
3. I absolutely HATE the "line of sight" mechanic in the game.
4. There's a very serious flaw in the premise of the game: you're directing a UN-sponsored defense team that is supposed to protect the ENTIRE WORLD from alien invaders, but you get minimal support from your sponsor nations. You're given less than a tenth of what is spent annually on the U.S. military alone. You're given almost no weapons or personel to begin with, compared to any other military force on Earth. You can't even get tips from the radar arrays that every NATO and former Soviet country has to aid in the detection of aliens.
All things considered, I can't help but feel that a lot of work has gone specifically into making this game arbitrarily hard, and the "story" does not nearly make up for that. I commend X-com for being a marvelously complex game, but that doesn't mean I want to play anymore.