How many bitcoins will there eventually be?
A pre-defined schedule limits the total number of bitcoins so that they gradually approach a total of 21 million (ignoring those that have been lost through deleted or misplaced wallet files). The limit of 21 million bitcoins is "hard-wired" in to the protocol, and there will never be more bitcoins than this:
Note that there are some assumptions built into the timing and unless the protocol is changed, they will actually be mined a bit earlier than this chart suggests.
Or later--if the value drops precipitously and difficulty takes a while to get low enough again. But the graph is a good rough approximation.
I think that's very unlikely. Even if there are a few precipitous drops, I think that will be outweighed by the overall trend of increasing hashing power (and they'll be followed be precipitous drops in difficulty). But, yes, that is possible.
I think saying "hard wired" is a bit misleading. The production schedule is coded in the software and could be changed to create more bitcoin. Fortunately anyone or any group that could change it is strongly incentivized to maintain the limit as it is integral to our idea of and trust in bitcoin.