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?
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!
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.