So, it seems like I'm not the only one with this problem:
julian@yggdrasil:~$ gnome-shell --replace
(gnome-shell:11309): Clutter-CRITICAL **: Unable to initialize Clutter: Unable to select the newly created GLX context Window manager error: Unable to initialize Clutter.
If I try to log in normally, GNOME fallbacks to Fallback mode
A bit of googling showed that this is ultimately reduced to a lacking feature in my gpu (nVIDIA GeForce 9500 GT), although this seems kind of weird, considering that I've been able to run Unity (apparently, users with the same problem also reported having trouble running Compiz).
I'm running the nVidia driver version 285.08.09, which seems to be the latest available. This computer has got 2 GB of memory, and uses a Intel Dual Core CPU with 1.6 GHz in each core.