Off the top of my head : the first and [url=https://www.gog.com/game/sin_gold]SiN.

Commandos' demo has the first and third level I think, and the latter is a massive level where the objective is to blow up a dam (in a not too spectacular way if I'm honest). I must have finished that level upward of 10 times in the demo. I remember I was actually kind of bored playing through that level when I finally got to play the actual campaign.
The SiN demo has the first level of the game I think (not sure), with a lengthy minigun-in-a-chopper sequence, which was only fun the first 8 or 10 times :P But the rest of the level remained a blast in which you had to clear a bank(?) of robbers. Shooters in actual real world locations were still a novelty for me back then.

Duke 3D

Oh yes played that one to death as well. It felt almost surreal to proceed to the third level for the first time

Max Payne.

Blood.

NICE 2 (Breakneck) also Robosaurs vs the Space B*st*rds. I also played the Monkey Island 3 demo alot back before I got the full game.

My brother and I spent an awful lot of time playing a demo of Sensible Soccer that I got from one of the British Amiga magazines. Great fun! :)

I had that on Amiga. Not being a fan of football, but I loved that game.

Warcraft II. It had a nice little taste of the game and after you beat it there was a screenshot and some text telling you to buy the full game which was personalized for aliance and horde ("Open the the treasure troves of your kingdom...")
Made me buy the game almost instantly (well, after playing the demo a few more times).

Jedi Knight II. It was a whole new level not present in the main game, with a pretty cool duel at the end (at least on hardest difficulty). I still sometimes play it when I just feel like I need a quick dose of lighsabre awesomness.

Wolfenstein 3D

Desperados: Wanted Dead or Alive. From Kellog's box

A bridge too far! ;)

I spent hours on Carmageddon splat pack demo, HOURS. Even if it was zombies instead of humans. Fortunately when I bought the game there was real humans with real red blood :psycho: