Previously, the strongest computer Go programs had reached roughly the level of a 10-kyu to 5-kyu player - well short of even amateur 1-dan level, which is a fair way below the level of professional players.
It looks like computers are catching up now, though - all thanks to programs based around Monte Carlo Tree Search. One program using MCTS is currently ranked around 5-dan on KGS. Recently, a team using the program "Zen" managed to beat a 2-dan (amateur) player in a best-of-5 series, 3 games to 1. More to the point, it looks like the algorithms seem to be highly parallelisable, so simply throwing more computer power at these programs makes them even stronger.
Interesting times in the Go world - probably a few years yet before the Go equivalent of Kasparov-vs-Deep Blue comes along, but I wouldn't want to put too much money on humans staying ahead now.
The other interesting bit of Go news that I saw recently - there's an Australian-born professional Go player. Her name is Joanne Missingham, and she moved to Taiwan when she was 4, and quickly moved up the Go ranks there. She's currently a 5-dan professional, and has done quite well in tournaments and leagues in Taiwan.
 There are two levels in Go rankings - "kyu", starting from 30 (for a raw beginner), up to 1, and "dan", starting at 1 and going up to 7 (for amateurs) and 9 (for professionals). To complicate things, the dan levels are not exactly equivalent between amateur and pro - it's generally considered  that the highest amateur dan levels are roughly the same level as 1-dan pro.
 At least, it was back when I used to follow these things - with the advent of Go servers on the internet, where amateurs and pros play each other regularly, and pro games are often played/relayed live from tournaments, it's possible that the top amateurs are a bit stronger relative to the pros now.
Original post on Dreamwidth - there are comments there.