We use on demand and have profiles for external, internal, dev/test, intranet , a/b testing, ftp logs....so only 6...but that is more than enough for me.
We are using On Demand - and initially rolled out with 10 profiles, but many more are planned for the near future.
We have 16 profiles on premise. I've been thinking about going on demand because it might be easier to stay on the latest release. We went to NI 188.8.131.52 but it required a lot of support. I'd be interested to hear from others about the costs / experience / benefits of on-demand.