Seems like everybody and their grandmother are holding a logo contest these days:
create.freedesktop.org is a project whose aim is to facilitate the sharing of things like code, media and infrastructure between various free and open source creative applications (think Inkscape, GIMP, cinepaint, scribus, Audacity and the like). They're going to be holding a logo competition. It's supposed to start soon. If you're looking to improve your Inkscape skills and stretch your creative muscles at the same time, then have a go when it starts. It'll accomplish both things. The contest is supposed to have started, but I see no confirmed details posted about it yet, but there are some tentative details over in the openclipart.org wiki.
Xmms2 as you might imagine is a project aimed at providing a followup to the venerable xmms media player application. They're holding a logo competition too. And in this one, they're offering a $400 Amazon Gift Certificate to the winner! This one has already started and entries are being accepted until the 13th of April. Drag your butt over to the Xmms2 Logo Competition page for details.
If you think you haven't got what it takes, I've got a small piece of advice for you:
Just drawing *something*. Anything. Don't go into it as something you have to submit on the first go-round. Once you come up with something, go get a coffee and stare at it for a while. Play with it. Before long you'll see what you like and don't like about it and you'll refine it (or even scrap it). But by that time your creative juices will at least be flowing. You'll then likely see off-shoots or completely different ideas. And even more importantly (IMO) you'll figure out different way of achieving the results you want. All the while, you'll be building your chops bit by bit. What is the worst thing that can happen by trying?
I am absolutely killer at throwing up obstacles to getting unappealing work started. I can be extremely creative in finding ways to avoid scary or potentially daunting tasks. But if I just summon up the willpower to do something (usually the easiest, shortest portion of the task), I quickly find myself achieving more and more progress. It's getting the boulder rolling that's tough. Once it's going you'll find it's a lot easier to keep it moving.
Cheers and good luck.