I've been trying lots of distros lately (openSUSE, Arch, Fedora, Ubuntu, etc.), and I have installed gnome shell on a few of them. AFAIK all of the distros' Gnome Shell packages are called "gnome-shell" (although I believe arch has a group called "gnome", but I think gnome-shell is still a package), so I think gnome shell is the appropriate term, especially when considering how Gnome 3 without the shell is used in Cinnamon, Gnome Classic, Consort, etc. As for using it, the last time I gave it a big try was on Ubuntu 12.04 with Gnome 3.4 right after 12.04 was released (and I used it for at least a week non-stop). I've tried Gnome Shell 3.6 in Fedora and 3.4 in Debian (which I also have installed right now, but I don't use it). I find 3.4 to be solid and, while I prefer Cinnamon and Xfce, I find it very usable. 3.6 seems to be less functional and intuitive, although I haven't given it a fair shot (I've only tried it briefly). Personally I see no improvements in 3.6 that particularly interest me, and it has gotten worse in some areas (I'm thinking nautilus specifically). Distros that I actually install are mostly Debian based (and 3.6 is still in experimental and will be for a while), and I keep a Mint LTS for steam and netflix. None of these distros have 3.6 yet, so I can't try it as thoroughly as 3.4.
Dell XPS 15 l502x - Debian Testing 64-bit NetInst Xfce, SolydX 64-bit Debian Testing, SolydK 64-bit SolydXK Testing
Old Gateway Pentium 4 Desktop - Arch Linux 64-bit Xfce and SolydX 32-bit Sid