When all 21 million bitcoins are in circulation, will there be any reason for mining? Is mining only useful for us "early adopters" or will it be a permanent part of Bitcoin?
Miners earning = block reward + fees
Miners will continue to get block reward in the next hundred years, but long before the reward "stops", the miners will get most of their earnings from transaction fees, so they will continue to have economic incentive to mine, when the block reward stops.
The way I understand it, the transaction fee that is automatically recommended by Bitcoin clients is distributed to miners.
That means, that even when there are now Bitcoins left to mine, miners still will earn coins because of the transaction fees. As far as I understand it, miners also serve the purpose to validate transactions and to ensure the integrity of the blockchain, and receive the transaction fees for this.