Well, this is indeed a problem for us too. What we did was to find people interested in the same things we were.
Some very talented people around here can both program their games and make their own graphics. I wish I was able to do that, but I'm not.
If you have a project you are working on, simply describe it and some people might want to join in.
If you ever decide to make a project that you want to sell, and decide to pay for the art, be VERY careful and don't blindly trust anyone. Ask for sample material, give the person some sample work that he should do, and never pay the full amount up-front! Set milestones and pay when the artist reached them.
This is experience speaking

Here's a funny one that happened on a project last year: Someone asked me for $95 (USD) just to draw 3 32x32 tiles, as a sample of what he could do, before the project was even started, and $55 for each tile that would be used in the final game.
We needed 250 tiles, so that's $13750 just for the tiles. Of course this guy was a real pro, and he made us a deal by lowering the price from $100 per tile to "just" $55.
Some people evidently don't live in the same plane of existence as many of us do.
Good luck!
--Eric