There are a multitude of go servers on the internet. Here's a brief list of a few common ones.
By far the most popular English-speaking server, KGS is a real-time (that is, you play your game in one go) server with a lot of features, including audio lectures by pros, tournaments, and a nice teaching interface.
Most of our members play on KGS, and the society has its own room - go to Rooms, Room List, then Clubs, and we're the University of Warwick Go Society.
The most popular international server, TYGEM
Of course, there are many other servers - IGS , DGS and OGS are other English real-time and non real-time servers, and there are many more Asian servers.