Came in to, worked on a SaaS product that did this in 2000 (it was around since '97/'98). I was doing new customer deploy and support, not direct development. It was running on MSSQL 97, I think, then moved to MSSQL 2000. It worked okay, but we moved away from that model in a "next gen" build around 2001/2002.

The biggest hurdles are in the things like configurations. You'll probably want to have one code base, and maybe even one deploy/package for web servers. However, you'll need different configurations for each customer (DB name, credentials, etc.) and a way to manage them, and a way to identify which customer an HTTP request goes to before you can process it. You can use things like host names in your web app, but you'll really end up wanting some kind of "request router" to manage everything...at that point, it's far easier to put everything in one DB and move on with revenue-generation.