I'm not considering bitcoins lost to people losing their keys, etc, that number is probably way higher than this one but it's impossible to calculate as lost keys might get found, etc.
These are burned coins, sent to a public address that has no known private key.
The addresses that I'm talking about look like 1BitcoinEaterAddressDontSendf59kuE, and are sometimes called burner addresses. Just in that single address there are more than 13 bitcoins. There are more than 400 bitcoins at 1111111111111111111114oLvT2, and so on. Here's a non exhaustive list of such addresses.
In case you're wondering, you don't have to trust anyone here, the long vanity public address tells you that it's virtually impossible that anyone in the planet has or ever will have a private key for that address.
I ran a small script to sum up all the bitcoins at those addresses and came up with a total of 3034.53041803 bitcoins.
This is a number that the vast majority of the population will never get to put their hands on, yet they're lost forever.
In the words of Satoshi Nakamoto:
Lost coins only make everyone else's coins worth slightly more. Think of it as a donation to everyone.