Here's a precious find I made a few years ago, that I still go to occasionally: Whomix is a collection of literally dozens of fan-made remixes of the famous Doctor Who theme by Ron Grainer and Delia Derbyshire.You can listen to them on the site by clicking for the "bloggable" version, or you can download them directly to your machine for a proper playlist pleasure. I've had a few over the years, like Skaro or Bust v.2.0 and Who Rocks the Party That Rocks the Tardis, but lately, I've been looking for a theme tune for my attempt at the Doctor Who RPG. I almost always use soundtracks for my role-playing games, and with all the Doctor Who soundtracks I have, it'd be silly not to. Except I don't want the Doctor Who signature tune itself, it's too recognizable. Instead, I wanted something that you'd notice was the same song only late in the game. My choice: Unreal Who by Miguel F Ettema.
PLAY IT HERE
It has an 80s feel, lots of different movements I can imagine would be this or that part of the show (sad, running from danger, triumph, etc.), though I admit it's a bit long. It could definitely be The Shepherd's theme (yes, that's what we think we may be naming our Time Lord).
Post-Time War, I think Who Am I?, a sad song with lyrics, also works... Might work it in at some point.
Hope you find something you like!