Bitcoin block #300000 was just mined today(blockchain.info)

    What is the maximum number of blocks?
    
    There is no maximum number, blocks just keep getting
    added to the end of the chain at an average rate of
    one every 10 minutes.

    Even when all 21 million coins have been generated?

    Yes. The blocks are for proving that transactions
    existed at a particular time. Transactions will
    still occur once all the coins have been generated,
    so blocks will still be created as long as people
    are trading Bitcoins.