Look there
Maximum number of records in a MySQL database table
mysql int types can do quite a few rows:
http://dev.mysql.com/doc/refman/5.0/en/numeric-types.html
unsigned int largest value is 4,294,967,295 unsigned bigint largest
value is 18,446,744,073,709,551,615
and there :
http://www.dbforums.com/mysql/378480-max-number-tables-mysql-database.html
The number of tablespaces will again be limited by your operating
system. Using NTFS on NT, the limit is 4,294,967,295. I imagine UNIX
will be limited by the number of inodes. However, before reaching the
physical limit of files you wil probably run into an issue with the
maximum number of 'open' files allowed.
My two first hit in google ;-)