Servers where you can play go against other people.
The K Go Server, written by Bill Shubert, comes with a variety of features which are not available on the telnet-based servers. Discussing games with other players is made very convenient.
A turn-based go server.
The Internet Go Server (IGS) was the first go server, and is still one of the biggest. Quite a number of professionals frequent IGS, and play there (mostly with anonymous accounts). Many of the Japanese title matches are broadcast on IGS. The web site contains information on the server and an art gallery which is well worth seeing.
On DGS you can play <b>turn-based</b> Go games. It functions more or less the same way as playing via email would, thus the games will take a few weeks.
DGS has 4,500+ users, spanning from 30 kyu up to 4 dan. Only a web browser is required, no need to install additional software. DGS is open source, free of charge, and has no negative side effects like advertisments, spam, etc.
A large go server
A turn based board game server.
A multi-lingual go server.
International Network Go Association
A browser version of postal Go or Mail Go, where you play Go with friends via postal or email. There is no time limit in the games of INGO. Usually it takes a few months to finish one game.
A turn-based server where you can play go (and chess).
It supports online human-against-human or against-AI. It also has a full-fledged ELO rating/ranking system as well as discussion board and in-game chat. You can use the site as guest player before registering.
Moreover the game is cross-platform, with web version, android and iOS apps, all connected to the same central server.