There are quite possibly hundreds of linux distros. I don't think there's any official list anywhere.
Personally, I use slackware or gentoo.
Slackware is the most unix-like linux out there, it's very fast and pretty damn stable. It's not too much hassle to set up (it's installation is great) and all in all, it works perfectly for my needs.
Gentoo, on the other hand, is a bastard to install. It's not long, but you've got to know what you're doing. It's very fast once it's installed - I mean BLAZINGLY fast. I could run GTA Vice City faster under linux using winex (the directx layer) faster than under Windows. That's pretty amazing in my opinion

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I wouldn't use Redhat or Mandrake personally - I don't really like RPM and I find that RedHat slows the hell out of my system. Nevertheless, it's not a bad distro for beginners.
Good luck