For the desktop, the best 'free' (as in zero cost) general purpose ones if stability isn't a concern, the likes of Fedora (Redhat's testing platform), Ubuntu (overhyped, bit flakey, not really any support) are sensible choices.
Sticking with general purpose desktop, but a bit less amateur, and a whole heap more stable, you'd be hard pressed to beat Debian. Will be a few months behind the less stable options above, but that leads to better testing, and greater stability. Debian makes a reasonable server as well, within the confines of the Linux kernel.
Then you are in the realms of the professional ones, 'free' but quite expensive. Redhat, SUSE EL, Oracle (basically a clone of Redhat, but with a search and replace on the copyright notices

), all more geared up for workstation and server use, which they do well (again within the limitations of the Linux kernel).
Then you get into the realms of 'proper' Unix, though many of these use non x86 hardware, although Sun do offer Solaris in an x86 version as well as Sparc.
All kernels are capable of long uptimes - I have plenty at work with 5+ yrs uptime (at OS level - hosted services been restarted frequently!) in Solaris, Linux and Windows. And at the OS level, Windows does appear to be the most stable
