I tried out the beta on Debian Linux, and it ran fine. I'd also plan to try it on Windows 2000, XP, and Vista. Its amazing that Firefox 3.6 runs perfectly on Windows 2000, but W2K is stuck with IE6, arguably the worst browser, ever!
I usually run Iceweasel on Debian, which is currently at version 3.5.9 for Debian Squeeze. I've run 3.6 on Ubuntu, which is supposedly much faster, but I didn't run a side by side comparison.