What is the actual likelihood that all of these 21 million BTC will be found? It seems to me, and I am not a mathematician, that at some point the time and cost of mining will be greater than the value of the bitcoins left to be found. I don't feel too bad asking such a newbie question, this being the newbie forum, so: what happens then? Is there an "Official Plan"?
Bitcoins aren't actually "found". They are paid to the miner who adds a block to the block chain. Currently the miner who adds a block to the block chain pays him/herself 50 Bitcoins. After there are 210,000 blocks on the block chain (we're in the 130,000s now) that fee goes down to 25 Bitcoins, every 210,000 blocks it halves again. So, eventually the fee will be below 1 BTC for adding a block.
However, blocks have to be added to the block chain, otherwise transactions cannot be confirmed. Without confirmed transactions, the entire system breaks down.
So, blocks will continue to be added.
Miners will continue to pay themselves, up to the full 21,000,000 coins.
Miners will continue to add blocks, even when all the coins are "found", because they will be paid by getting to keep all of the transaction fees that are on the transactions in the block (which is why there HAVE to be transaction fees, think of it like a sales tax paid to the miners).