Canonical has begun posting videos of Mir in action. While Mir itself doesn't do much yet, a video by one of the Mir developers shows Unity running on Mir. But it's running Unity through an X Server via the "XMir" project.
His most prominent video is showing the Unity desktop running on Mir, but it's through XMir. The full Unity desktop hasn't yet been rewritten in Qt/QML and made to run on Mir, so this is running through XMir. XMir is to Mir as XWayland is to Wayland.
XMir is basically an in-session root-less X Server running atop Mir. This is how legacy X11 applications will continue to be supported by Mir and is the same approach that Wayland developers did for running X applications on their display server. Neither XMir nor XWayland have been merged into the mainline xorg-server, though XWayland is on approach soon as a few more things are settled hopefully during the xorg-server 1.15 merge window.
So here's the video of Unity running on XMir:
Thomas Voß also posted a video of Ubuntu Touch on the Galaxy Nexus 7 and running Mir as the compositor. Mir is running in replace of Google's SurfaceFlinger with Android. Thomas notes that Unity is not fully integrated and is rather a preview. Mir is not using a hardware compositor but just OpenGL ES. The Qt support for Mir is provided by the unmerged QMir bindings. As noted earlier, Canonical intends to provide Mir patches for GTK3 and Qt5 against their master branches, but they don't plan to go back and provide official support for GTK2 or Qt4 (nor has support for any of the other tool-kits been mentioned).
Lastly, Thomas posted a video of some native OpenGL applications using EGL running on Mir, albeit it's not entirely exciting:
While it doesn't show anything exciting for Mir, at least it's better than the stock Mir accelerated demo:
At this point, Wayland is still doing much more than Mir.