Our last annual tally of ~400 known "burn addresses", that is bitcoin addresses with almost assuredly no known private key, totaled 2,759.42507135 BTC as of Dec 2017.

2017
https://bitcoinwhoswho.com/blog/2017/12/30/8-97-bitcoins-burned-in-2017/
2016
https://bitcoinwhoswho.com/blog/2016/12/21/btc-burn-addresses/