I never tried it, but owning a raspberry pi I can say to a certain extend that the RAM on the Pi is not by far sufficient enough to provide a stable running server. Especially not if you want to serve more than 1 user at the time.
Also consider that the Pi itself has an ARM architecture and relatively slow processor. There might be an Odoo or OpenERP version built for it, but I think it is not actively maintained.
If budget is an issue, it might be better to look out for an older PC somewhere and help yourself to some spare ram. This is going to perform a whole lot better.
Thanks Ludo!!
@Nelson, I agree with Ludo on this, I think you would find it unusable given the default pi specs out of the box. Odoo used a modified pi for their POSBox campaign, although I think it comes with significantly better specifications. It may be workable however with several pi's in a cluster, eg.: http://raspberrywebserver.com/raspberrypicluster/raspberry-pi-cluster.html However the cost to benefit ratio on this would probably lean in favour of just purchasing low-end desktop computer parts.
Since this question was posted in 2014, it would be interesting to revisit, even more specifically:
Has anyone tried to install Odoo on a Raspberry Pi 400?