All bitcoins issued have been (and ever will be) issued come as the result of mining.
Currently that reward is 50 BTC per block. So the total can be calculated as 50 times the current block number shown by your bitcoin client, or from Block Explorer, for instance:
http://blockexplorer.com/q/getblockcount
e.g. the current value is 128,405.
128,405 times 50 = 6,420,250 bitcoins.
[Edit: The block "count" starts at 0 so to get the correct number would need add another 50 for that block as well].