Escaping single quotes (‘) in Transact-SQL is done by replacing the single quote with two single quotes. So:

SELECT 'I went to Kinko''s'

Returns “I went to Kinko’s”

The only case where two consecutive single quotes don’t return a single quote is when the first one also starts the string.  In this case, if only two single quotes are present, the second one ends the string and the return value is the empty string.  SQL Blog Casts has a good example of this.

Doing the same in MySQL

Escaping a single quote in MySQL is done by adding a backslash before it (\’)

SELECT 'I went to Kinko\'s'