Mysql is more complicated to be evaluated in this sense than other Dbms because the storage engine influences the capabilities of the database.
For example, Mysql itself has no table limit, being limited by the chosen file system. However, if you use Innodb as a storage engine, it is limited to 4 billion tables (32-bit integer without signal).
In the case of table size, using a modern file system, the limitation is a bit absurd: using Myisam, you can have table up to 256TB, if the file system supports (today, any modern FS - aka NTFS, ext4, xfs, etc - supports at least 2TB, being common they support 256TB).
Anyway, overall, there’s not much to worry about as long as you don’t work at the LHC, which generates TB of data daily.
The most important thing is to use the most modern versions of both the Operating System and the File System, as well as the DBMS (and obviously use the most appropriate DBMS for the task).
More details on Mysql boundaries, see the official documentation:
https://dev.mysql.com/doc/refman/5.0/en/limits.html