Basically a duplicate of this question. It comes up a lot, and the remove category base functionality probably should be an option in WordPress to be honest.

Here was my answer from there:

No Category Base plugin to remove the /category/ bit from the URL.

:)

If you have a page with the same name as a category, the page will be shown instead the category archive, but the URLs of posts won\'t be affected. At least, that used to be the case. I think I heard news of a recent change in the way WP calculates permalinks (for the better).