I've used Fedora since version 6 and Ubuntu since 6.10, and they are both pretty good. I'm using the 64-bit edition of Fedora now, using Java (with support for applets) and Flash fine, along with being able to play music formats such as mp3 and watch movies in forms such as mpeg (just to give you an idea that I got stuff to work on Fedora 8, and to make it harder, the 64-bit edition of Fedora 8). In addition, with the help of some proprietary software, I can use things like Compiz Fusion and play 3-D games such as OpenArena. Besides what anybody else may have said, one of the main reasons why I use Fedora is because a lot of the software I use, such as KTIGCC and CodeBlocks, and other stuff is available in the convenient RPM form, making it very easy to install and upgrade, while they aren't available for Ubuntu (there is a Debian repository at calcforge.org, but the .deb packages might not work completely perfectly on Ubuntu, and there isn't an automatic repository configuration package like there is for the Fedora RPM repository).
If you have the time and are willing to put in the effort, I recommend trying multiple distributions and seeing what you like. If you don't feel very comfortable with GNU/Linux or don't want to spend a lot of time compiling programs and stuff, I'd avoid Gentoo-based distributions (although besides having your programs possibly be a little more compact and faster because of them being compiled, you'll probably also learn a lot more about how GNU/Linux and computers as a whole work - I know from experience). If you want something that's easy to use, I'd recommend Ubuntu. LinuxMint, a increasingly popular Ubuntu-based distribution, and PCLinuxOS are supposed to be pretty good too, but I haven't tried them out, so I don't really know. I tried OpenSUSE and Mandriva too, and they seemed decent, but I only used them for a short time. And then, there's Fedora, which I currently use. It might take a while to get things you might take for granted to get working (such as Flash and an appropriate 3-D driver), but this is mostly due to that Fedora is strict with being completely free, so it doesn't include proprietary software - even in its repositories (unlike Ubuntu). Fedora 8 does come with
IcedTea now, which basically takes care of any previous issues of getting Java to work, particularly applets.
I suggest going to
DistroWatch to learn more about different distributions.
In addition, don't limit yourself to GNU/Linux - there are also free variants of BSD - freeBSD being the most popular - and other free operating systems such as OpenSolaris.
And lastly, I recommend you hold on to your Windows CD, in case you want to switch back or dual-boot.