Total circulation will be 21,000,000 coins.  It'll be distributed
to network nodes when they make blocks, with the amount cut in half
every 4 years.

first 4 years: 10,500,000 coins
next 4 years: 5,250,000 coins
next 4 years: 2,625,000 coins
next 4 years: 1,312,500 coins
etc...

When that runs out, the system can support transaction fees if
needed.  It's based on open market competition, and there will
probably always be nodes willing to process transactions for free.

Satoshi Nakamoto

On the Instability of Bitcoin Without the Block Reward

Bitcoin  provides  two  incentives  for  miners:  block  rewards and transaction fees.
The former accounts for the vast majority of miner revenues at the beginning of the system, but it is expected to transition to the latter as the block rewards dwindle.   There  has  been  an  implicit  belief  that  whether miners  are  paid  by  block  rewards  or  transaction  fees  does not affect the security of the block chain. We show that this is not the case.  Our key insight is that with only transaction fees, the variance of the block reward is very high due to the exponentially distributed block arrival time,  and  it  becomes  attractive  to  fork  a “wealthy” block to “steal” the  rewards  therein.   We  show  that  this  results in an equilibrium with undesirable properties for Bitcoin’s security and performance, and even non-equilibria in some circumstances.  We also revisit selfish mining and show that it can be made profitable for a miner with an arbitrarily low hash power share, and who is arbitrarily poorly connected within the network.  Our results are derived from theoretical analysis and confirmed by a new Bitcoin mining simulator that may be of independent interest.
We discuss  the  troubling  implications  of  our  results  for Bitcoin’s future security and draw lessons for the design of new cryptocurrencies.