How many bitcoins are there currently in circulation?
If you are running Bitcoin Core, you can see the total amount in circulation using the RPC call gettxoutsetinfo (in the Bitcoin-Qt debug console, or using bitcoin-cli if you run bitcoind).

At the time of writing, the output is: 
{
  "height": 517245,
  ...
  "total_amount": 16965398.58586455
}


which means there are currently ~17 million BTC in circulation. This number takes into account certain types of destroyed coins.

See also this answer of mine about how many there will eventually be.