Without being completely overwhelmed at the overly opinionated design substructure known as typography, the following are my personal favorite sites to find good, free font downloads for basic and professional uses:
While this site isn't a free-download site, it is royalty free, and a co-op for typeface designers. You pay what you feel is appropriate for what you want, and 100% of the proceeds go straight to the designers. They worked hard so you could have just the right styled lettering to portray the energy and angst for that garage band promotional poster, and they should get paid for their work.
Not only is this a dwindling online approach to making a living, but it's giving you the opportunity to be a decent customer if you have the means to be, and offering it free if you don't. This is a lost value for most these days, but no one should be denied good art for the sole reason that they can't afford it.
I've mentioned the illustrated works of the fabulous Matthew Inman before, and I can't ignore him in this post either. He was kind enough to list a few of his selected fonts that are used regularly on his humor site The Oatmeal. Not only that, but they are also free. These are mostly appropriate for humorous uses, and less professional in style, but still have value depending on the application.
Simple, and easy to search fonts, categorized by themes and styles, free to download, and an emphasis on the authors. This site has the option for you to donate to the author of each font, as well as having each authors personal website associated with the font listed in their catalog. They also allow font submissions, and have a forum for user questions, font identification, and discussions.
The range of styles on this site is what really gets me excited, and it's organized layout. I can search by name alphabetically, or jump through the theme categories if I have a specific look and feel in mind.
Lower in the legitimate ranks, 1001 Free Fonts gives you just what they promise, and several spammy side-links to other similar sites of questionable taste. It's good on its word though, and sometimes you just need a quick inspirational typeface to get a direction for a project.