In one of the stackoverflow podcasts (#18 I think) Jeff and Joel were talking about multi vs single tenant databases. Joel mentioned that \"FogBugz on Demand\" used a database p
Joel has talked about this at another place (sorry, no reference handy) and said that before switching to MS SQL 2005 the management console (and the backend) had problems attaching more than 1000 or 2000 databases. It seems that 2005 and probably 2008 again improved on these numbers.
As for all performance questions are always dependent on your actual hardware and workload an can only definitely answered by local benchmarking/system monitoring.