There's no question for me, it was Bioshock on 360. After I played, I had no doubt I was going to to get that game. It demonstrated every important detail of the game while still getting you to beg for more.

The Resident Evil 4 demo was certainly the most convincing demo that i've ever played, but i tend to have a good sense of what games I'm going to like without playing them, so i've never been a big demo guy.

Does shareware count?  Doom 1 shareware was the greatest thing ever.  Played that for YEARS before I even bought a copy (disks got sent snail mail).  Bought Doom 2 before I had all of Doom 1.

I remember when REAL 'demos' started cropping up.  Sega Rally for PC was one of the first I remember.

I really liked the Dead Rising and Lost Planet demos on 360.  Bioshock was big but I was already hyped to the sky for that game.

People posting below reminded me of some more : Crackdown demo was great, Metal Gear Solid 2 demo I played a lot.

Well, Bioshock was one of my favorite demos, and I also liked the Strangehold demo. It pretty much contained everything you needed to know and experience in the game in one level. I would suggest playing that instead of buying the game ;)

Metal Gear Solid, 1998 on PSX. I was absolutely stunned and blown away.

Bioshock demo was awesome, but doesn't hold a candle to the impact the MGS demo had on me.

The Skate demo, I played it for like 10 hours.

I thought the Crackdown demo was really good.  Also the Left 4 Dead demo pretty much sold me on that game.  I hadn't really been following the game before playing that.

Either Lost Planet or Patapon 2(I've spent more than 3 hours on this one).

I really don't play many demos. I thought the demo for Mat Hoffman's Pro BMX was awesome. It was included with Tony Hawk's Pro Skater 3. Unfortunately the final game ended up being a little bit disappointing, and that warehouse level that was in the demo was altered a bit, for the worse.

I thought the Dark Cloud demo I got when I bought my Playstation 2 was frickin awesome!

"The Skate demo, I played it for like 10 hours."

Skate

As it's been mentioned before, the Skate demo had me addicted for at least 10 hours.  Probably the most convincing demo I've played.

Zone of the Enders: The 2nd Runner.

MGS2  The tanker demo.

Deus Ex on PC. They gave you the entire first mission, and the number of ways to tackle it floored me. I went out and grabbed the game the same day.

Tony Hawks Pro Skater demo for PS1

Legend of Zelda:  Wind Waker

The Civilization Revolution 4 demo for the PS3. It made me love the game and want to get it. 

RE5 it made me buy the game

First time i played the demo for Worms 2 i played it over and over again.  The Demo for Battlefield 1942 and 2042 i played a great deal of and on the Xbox 360 i played the Skate demo over and over.

Worst demo...The original Fallout...i remember having no idea what was going on and had no interest in the game...only years later did i play Fallout and realized how great it was.

Killzone 2 demo. i lost count at how many times i played it. i have never re-played a demo that much before.

Final Fantasy 7 demo, at the time those 3d rendered summons blew my mind, MGS demo is my first runner up