What I look for in a Linux distribution:
1) Stability of the basic operating system is crucial, of course. By that I mean I should never see "kernel panics," failure to boot, or what is known in the Windows world as the Blue Screen of Death. (To be honest, I haven't seen a BSOD for several years, even when running Windows.) Failure to boot... well, that's another story, most of the sorry details of which I brought upon myself.
2) It has to look classy, which for me, at the moment, means KDE 4.x.x.... that is, the latest version of the K Desktop Environment. Those in the know may be asking "what about that stability you were talking about?" Well, I have had relatively little trouble with KDE 4.1 on my current setup. I am a visually oriented person, and I like the glassyness and the transparency effects of KDE 4. My only real dissatisfaction with it at this point is the few applications I use regularly which are still using the KDE 3.5 libraries, such as OpenOffice (office suite) and Amarok 1.4.10 (music player).
3) Quick access to a large repository of software packages. This generally means Synaptic, or a similar graphical tool used for sorting, selecting and installing of Linux software packages.
4) Frequent visits to major news websites these days requires the latest updates to FlashPlayer, Java, etc.
5) A large user base, with good online documentation, such as a wiki, and with a friendly user forum where I can go to get help with technical problems.
6) Ongoing development. I prefer not to wait a year for patches and upgrades.