How many rows can a database handle?

It depends on

1. database limits
2. hardware limits

see

The internal representation of a MySQL table has a maximum row size limit of 65,535 bytes, even if the storage engine is capable of supporting larger rows. BLOB and TEXT columns only contribute 9 to 12 bytes toward the row size limit because their contents are stored separately from the rest of the row.and Oracle allows two bytes for row numbers, so theoretically they could go as high as 65535 rows in a block.

However, given the minimum row length (11 bytes) and maximum database block size (32K), the pratical limit on the number of rows in a block is in fact only 2970.