If you've entered an unterminated query, it doesn't run, and that's why typing exit doesn't work - MySQL thinks you're still in the middle of a query.
Watch out for copying and pasting queries with strings from a word processing package - quotes may have been replaced with 'smart quotes' and this will mess up your query. You also need to have terminated any strings in your query. Only when you enter a semi-colon will the query be executed.
SQL supports queries entered as multiple lines.