Check this out: https://en.bitcoin.it/wiki/Controlled_supply#Projected_Bitcoins_Long_Term
It states that new coins can be mined even in the year 2140.
Johanakerblom, when the block reward is 1 satoshi and it is halved, it will go to 0 satoshis. No more bitcoins will be created at that point.
I belive Satoshish are divisable.
I read this:
"The current level selected in the code (by Satoshi) is 8 decimal places (1 satoshi = 0.00000001 BTC) hence the nickname for the smallest unit currently possible for bitcoin today.
As a thought exercise, if a consensus of the network (miners, but also clients and server applications for compatibility reasons) decides to update to a version of the protocol that includes 16 decimal places inspired by your post, we could end up with a new base unit (1 satoshi = 100,000,000 gracchi) as well as nanobitcoins (nBTC), picobitcoins (pBTC), and even femtobitcoins (fBTC, 10 gracchi)"
Here:
http://bitcoin.stackexchange.com/questions/19661/how-is-bitcoin-infinitely-divisible