At the increasingly slow rate that coins are produced, this won't happen for some. But assuming that bitcoins are still around and in use at the point in time in the future when this happens, what will be the effect of this?
The supply is fixed and no more can be produced; and since it's still around, chances are there is demand / usage that would likely grow. The likely result seems to be that from that point onwards, bitcoin's value would only grow to due an increase in its scarcity. Perhaps, this is a possible justification or rationalization for bitcoins as a (very) long term investment.
Also, not too familiar with the internal bitcoin protocol but what will happen to the network of miners who help with verifying / maintaining the transaction ledger? I think the reason they participate is that they are (proportionally) rewarded for their services in new bitcoins. When this is no longer the case, who will agree to do this work then?