It probably depends on the version of SQL Server, but in theory, you could have 32,767 databases per instance:
Maximum Capacity Specifications for SQL Server[
^]
But...would the rest of the infrastructure support that many requests? I think you'd need to look closely at the whole "probably traffic" you expect to be generated, and plan accordingly. I wouldn't try putting that many DBs on a single SQL server instance, even if it was a major server farm!