Yes, there's a certain amount of raw artistic talent involved in design, but you can get a lot of the way with two rules:

1) Be Simple. 2) Be Sparse.

You don't need drop shadows, shiny buttons, gradients, rounded corners, animation, or complex imagery to make a good site. As any good musician will tell you, music is about what you do with the space in between the notes; graphic design is about what you do with the space around the content (and if your content is good, the less crap you need to put around it!)

If you use a simple layout, a very small palette of 4-8 colors, 1 font, and only a few font sizes, you'll find that your designs will improve automatically. If you lack even the basic ability to coordinate colors, use a tool (http://www.colorschemer.com/schemes/ is a good source), and never deviate from the scheme that you choose.

Remember: think Google, not Microsoft.