I skipped Mass Effect 2 because of the demo.

Ughhh... you brought me back bad memories.
I think the only time was when I was casually in a Wal-Mart, I saw Sonic Rider's for GC, and really enjoyed the demo, it was fun, fast paced and the gameplay was good. So I got it.
What a piece of crap, the modes were terrible and the game got old very quickly.

Doom, Duke Nukem 3D, Whacky Wheels... ah the days of shareware...

games I bought because of demo:
NBA Street Vol. 2
Stubbs the Zombie
Armed and Dangerous
Crackdown 2
Lost Planet
Ninja Gaiden 2
Shadow Complex
Crysis 2
ilomilo
Beyond Good and Evil HD 

There are more, but this is all I can remember. If I see a game I'm interested in I always download the demo. Huge part of my decision making.

After playing the demo of Armed and Dangerous on Xbox and laughing so hard I literally rolled on the floor, I preordered as soon as I was able to breath.

Enslaved demo put me off.
and also i preordered Dragon Age 2 because i loved Dragon Age:origins, but that demo really put me off yet i kept my preorder to give it a chance. The game lasted 3 days when i got it and i traded it in.

Games I bought after playing demo:

Just Cause 2
Mafia II
Halo Reach (beta)

Games I stayed away from after playing demo:

Battlefield 3... just didn't really enjoy it. And the sheer bugginess of the beta didn't help matters.
Crackdown 2... was kinda interested after hearing good things about the 1st one, but this was not my cup of tea either.
Crysis 2... graphics looked great even for multiplayer, but I knew I wouldn't be playing it for very long so I skipped out on a purchase.

Edit:  trunkswd reminded me of that god awful game Too Human.  I played the demo and was like, this is what we waited three console generations for?  A horrible generic dungeon crawling and looting game?  The worst part is we'll probably never get a proper sequel to Eternal Darkness because of how poorly this game did.

Yes. I used to have an OPS2 subscription back in the day and I remember several demos I played and went looking for the full game (I was only 10-13 at the time). Jak 1, Sly Raccoon off the top of my head, and just this month, I bought a 360, and played a demo for Forza 4. Yesterday, my copy of the game arrived.

I even bought my first console because of a demo. I played my older sister's PS1 on a demo disc which had WipEout 3 on it. I then asked for the console for Christmas and soon had Wipeout 3, which is still my favourite game ever made to this day.

I bought Tekken 4 because of the demo. Or more specifically, because I was a horny 10-year old and the demo had Christie as a playable character.

I regretted it as soon as I grew a brain and realized that I hate Namco fighters.

the halo demo is really popular even still.