Update 2014-12-05
I am not recommending this approach due to reasons laid out in Simon's (accepted) answer as well as Diego's comment. Please use query below at your own risk.
Original answer
The shortest one I found on MySQL developer site:
SELECT Auto_increment
FROM information_schema.tables
WHERE table_name='the_table_you_want'
Mind you if you have few databases with same tables, you should specify database name as well, like so:
SELECT Auto_increment
FROM information_schema.tables
WHERE table_name = 'the_table_you_want'
AND table_schema = 'the_database_you_want';
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