Ubuntu is the current flavor that gets attention for "ease of use". I usually recommend starting with that, then if you want to try a few more, trying Mandriva and OpenSuse. Different flavors, but fairly equivalent to Ubuntu.
Once you've played around a little and feel comfortable, you can try using Gentoo and configuring EVERYTHING. :) It takes a lot of time, but you have (virtually) complete control of your OS.
If you have any experience with any of the Unix flavors, you might consider trying Solaris 10, as it is now freely available. However, I don't think Solaris is as usable for Desktop Computing as the others mentioned above. Solaris gives you a lot of power and works well as a server OS. I know my father uses Solaris 10 on one of his systems, but I don't think he uses that system as a primary desktop system, so YMMV.