I wouldn't say a couple hundred. Maybe on some hosts, but that's pushing it.
They may offer a ton of space and bandwidth, but they're really monitoring CPU time and DB connections/queries/size.
In fact, I'm going through this with a client as we speak.
Their site was running pretty slow a good bit of the time. After optimizing as much of their plugins and such that I could, the only thing left would be to break up the database. I had them ask their host (who claims you can create unlimited databases) if they had a problem with a couple hundred smaller db's, vice one big one.
Here's an excerpt of the communication, names changed to protect the innocent.
Question:
Fred asked: "I am running a wordpress MU on your server and am getting performance problems. My developer has recommended I create multiple dbases to help lighten the load.
Do you allow this? There will be a couple hundred dbases."
Response:
Host replied: "I checked with our MySQL admin and he very strongly discourages this.
Actually he very strongly discourages the use of MU on the shared hosting environment, mostly because of the way it continues to add large amounts of tables to the database. Basically it starts to cause daily backup issues and degrades the performance across the entire server.
He mentioned that once it grows past about 500 to 1000 tables it'll be causing enough problems to warrant disabling your site, and recommends moving to a dedicated server for any serious use of this software."
I highlighted a couple places of interest in the reply. Specifically, the max tables before they kick you, and their recommendation in terms of hardware for using this software (MU).
That isn't from a fly by night host, although they "offer the moon to make it sound good". That's from dreamhost. (Popular, but not what I would personally consider reputable.)
Remember that every blog add 8 tables by default, without any plugins, plus you have your global tables and the primary blog as well (9 tables). So you have 17 to start with, without a single signup or plugin. That gives no more than about 100 blogs at their max (without plugin tables), and 50 or so before they may kick you.
However, you'll have performance issues before that most likely.