Here's a music writing challenge I've done a few times, which I've found incredibly useful so far.
The challenge is this: you have 24 hours to write a piece of music. Completely. That's it. It can be as long or as short as you like (although completing a Wagnerian epic in 24 hours might be a little ambitious), just so long as it's a piece of music written to a level that it could reasonably be performed and not baffle the audience as to why you bothered, while you shout out "pretend there's a really cool bass solo for the next 8 bars". You can record it if you want and have the time/equipment, but that makes the 24 hour limit much more restrictive, and it's not really the point. It can have lyrics, it doesn't have to. It's up to you.
You can, of course, revisit it after 24 hours, that's not the point. That deadline is there to make sure you get something finished, and to a certain extent, polished. It's there to force you to develop your ideas, not spend all your time searching for that perfect base idea. Even if it ends up rubbish, you learn far more from fully developing everything else around your core idea than you do from getting frustrated, putting your half-baked idea in a box and saying "I'll come back to this later...".
I use Guitar Pro for this as it makes it fairly easy to transcribe things, and, better, it plays them back for you with synthesised instruments of varying sound quality (it does clean and light distortion really well, heavy distortion not so much, but it's either that or MIDI. Drums sound great though).
Here's some stuff I've come up with doing this, which I'm pretty pleased with (you'll need a fairly modern browser to hear these and IE probably won't suffice):
Fairly straightforward metal. I'm happy with the flow on this, but the leads don't seem to quite work out quite as they could. Not sure if that's the note choice entirely or whether the really awful guitar tone gets in the way. The rhythm is very strong though.
Slightly Ennio Morriconeish, well okay, the middle part is more than slightly. I'm pleased with the time change towards the end while keeping in with the western theme.
Minimalistic bass driven bluesy-rock. Again with a hint of Morricone. It's entirely possible the snare drum makes no sense. Listening to it again now, I have no idea. I thought it was rubbish when I wrote it but it seems to grow on you.
This too was supposed to be minimalistic until I threw in all the spacey arpeggios. I think some of it could benefit from the sound being fleshed out more, it seems a bit sparse, but not too bad otherwise.