How many bitcoins are there currently in circulation? Where do I find the total number of bitcoins currently out there?
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.