The final 0.00000001 BTC will be mined on March 2, 2138.
You can hold me to that. If it does not happen on that exact date look dig me up and I will give you $1000 worth of BTC. Of course that will be exactly 0.00001 BTC on that date. You can hold me to that also.
Burtw is essentially right. Most (98%) of the "complete" bitcoins will be mined by 2050. So by 2140 there will essentially only be a satoshi or two. As the block rewards keep getting cut in half, the last fifty years you are slicing fractions of a bitcoin. This argument has been discussed several times, but this thread link has some charts which may put it more into perspective for some members:
https://bitcointalk.org/index.php?topic=235926.0