GNOME 3.10 presented initial support for running on Wayland without any X11 dependencies. In my GNOME 3.10.x testing to date atop its Wayland compositor the support has been decent when using the open-source Intel driver (other GPU drivers are more iffy) but there's still occasional segmentation faults with Wayland Mutter and other problems. Some GNOME applications haven't yet removed their X11 dependencies so they are being piped through XWayland. With GNOME 3.12 (due out in March 2014), the support will be much better.
Matthias Clasen of GNOME has now blogged about the continued Wayland porting process. Some of the recent work that you can look forward to with GNOME 3.12 on Wayland includes Wayland sessions in the GDM display manager, keyboard handling, pointer handling, greater window management support, better application support, and a lot more GNOME application/porting. See Clasen's blog post for many more details on the current state. Beyond his comments, further information can be found via the GNOME Wiki.
It appears that GNOME 3.12 is making very good progress on shipping a stable GNOME Wayland-based Linux desktop experience, after which one of the first platforms where there's expected to be this support will be Fedora 21 (likely as a beta experience and defaulted for Fedora 22 if all goes well). 2014, the year of Wayland?