Good one.

You can select the W3 demo levels in The Frozen Throne as well.

The God of War demo was a dating sim, you can´t imagine how disappointed I was when the actual game was released as a hack´nslay with my screen being full of flying limbs and intestines. :(

How did I not know this!?
*downloading*

Wing Commander Prophecy demo had a unique 3 mission mini campaign, with 2 different versions of the last mission depending on how you did on the second mission, and cinematics, forming a prelude to the main game. There's a version with fan-added OpenGL support that should work on post-Win98 machines:

http://www.wcnews.com/wcpedia/OpenGL_Demo

I remember trying the first demo for Stronghold, from the CD on a magazine. It was actually another game, "Castle Attack", showing screenshots of the game below the play area. It seems to come with the game on GOG.

I think this counts as "wholly original from the game".

Couple others I found, Jazz Jackrabbit and Lemmings both had original Xmas-themed demos/freeware/shareware.