I heard that in general, you don't see a single server running sqlserver having more than 100-150 databases on it.
Is this the same case with mysql or postgres?
The most I've ever seen on sql server instance was 3500 databases, just shy of a petabyte total data. It was interesting to see a windows sql cluster with a dedicated SAN. On a side note there was also an analysis services cluster with it's own dedicated san as well. I have no idea how many cubes were on that instance.
As I rarely deal with mysql (I've only done migrations from mysql to sql server) and have never dealt with postgres I can't comment on scalability of those platforms. The biggest mysql server I've seen was 10 DBs with about 4 terabytes of data total.
number of databases is an irrelevant measure. It's more to do with the number of user connections, the query load & the size of the database.
According to this SQL Server can have 32,767 databases attached to it. You probably won't see this in production, but it is possible!