Are there any limits on length of string in mysql?

CHAR

A fixed-length string that is always right-padded with spaces to the specified length when stored The range of Length is 1 to 255 characters. Trailing spaces are removed when the value is retrieved. CHAR values are sorted and compared in case-insensitive fashion according to the default character set unless the BINARY keyword is given.

VARCHAR

A variable-length string. Note: Trailing spaces are removed when the value is stored (this differs from the ANSI SQL specification)
The range of Length is 1 to 255 characters. VARCHAR values are sorted and compared in case-insensitive fashion unless the BINARY keyword is given

TINYBLOB, TINYTEXT

A TINYBLOB or TINYTEXT column with a maximum length of 255 (2⁸ – 1) characters

BLOB, TEXT

A BLOB or TEXT column with a maximum length of 65,535 (2¹⁶ – 1) characters , bytes = 64 KiB

MEDIUMBLOB, MEDIUMTEXT

A MEDIUMBLOB or MEDIUMTEXT column with a maximum length of 16,777,215 (2²⁴ – 1)characters , bytes = 16 MiB

LONGBLOB, LONGTEXT

A LONGBLOB or LONGTEXT column with a maximum length of 4,294,967,295 (2³² – 1) characters , bytes = 4 GiB

See MySQL Data Types Quick Reference Table for more info.

also you can see MYSQL – String Type Overview