Qtopia on Neo1973
Get "Qtopia on Neo Flash Image and kernel" from here. Currently the flash tarball has the 2.6.21 openmoko kernel and a Qtopia phone edition jffs2 flash image cross-compiled for the Neo.
Newer unofficial Qtopia images can be found in the ScaredyCat repositories.
It appears you must clear the flash chunks first (if you have not updated your uboot. If you have, you may skip this step). Get into uboot console  and enter
nand erase kernel nand erase rootfs
Download and use dfu-util as normal and the ip address and cidr are the same as the openmoko build (192.168.0.202/24) :D - Simple, Eh?
Qtopia AND OpenMoko
Why choose when you can have both ;)
I assume you allready have some recent version of OpenMoko on your Neo1973. If not, have a look here.
First backup everything on your micro-sd card you don't want to loose as we are going to create a new filesystem on it. This is necessary beacause vfat doesnt support links. Then ssh to your neo and do:
umount /dev/mmcblk0p1 mkfs.ext3 /dev/mmcblk0p1 mount /dev/mmcblk0p1
On your desktop: Get "Developer root filesystem" from here. Get the opt/Qtopia folder plus the qpe init script out of the archive repack and copy it to your neo. One could do this like this:
tar xzf ficgta01-qtopia-developer-rootfs.tgz opt/Qtopia etc/init.d/qpe mv opt/Qtopia etc/init.d/qpe . && rm -r opt etc tar czf Qtopia.tar.gz Qtopia qpe scp Qtopia.tar.gz firstname.lastname@example.org:/media/card/
On your neo again: unpack the archive you just copied and link the Qtopia folder to /opt/Qtopia. Then move the init script to /etc/init.d/:
cd /media/card tar xzf Qtopia.tar.gz mkdir -p /opt ln -s /media/card/Qtopia /opt/Qtopia mv qpe /etc/init.d
Now kill the x server and gsmd and start Qtopia (this can take some time):
/etc/init.d/xserver-nodm stop /etc/init.d/gsmd stop /etc/init.d/qpe start
Where from here? You could put the last step in a script and start it from a terminal on your phone. But much nicer would be if you could choose between both interfaces on init time and have some small application in Qtopia/OpenMoko to switch.
Build your own
Most things seem to work out of the box, however you may need to use the following command to get audio:
alsactl -f /etc/alsa/gsmhandset.state restore
Or put this command in /etc/init.d/qpe line 64
Do not switch themes. Only the default theme is usable. For example, once you switch themes, the lock feature continues to work, but only if you unlock using the smallest # keypad in the world.
Suspend support is very flaky. The neo often shuts off from a suspend state. It will not wake from suspend for an incoming call or text message (someone try setting an alarm and report results here). To turn suspend off (this will of course use the batteries very quickly), hit the down arrow next to the suspend setting in the power management until it says "Off".
When using the virtual keyboard, do a quick flick up or down over the keyboard to access numbers/symbols/capitals.
In summary, Qtopia on the Neo1973 is much closer to being ready than OpenMoko as of this writing. However, sound and suspend support prevent it from being at all useful as a cell phone (as a landline that doesn't ring but instead vibrates, it works ok).
Here are some screenshots of Qtopia runing on a Neo 1973. Personally I find it very impressive...
For full size videos, 346 MiB: