www.online-go.com
It is no secret that I am an OGS guy. So an argument can be made that I am not objective, but to my knowledge it is the only server where you do not have to download anything, supports both live and correspondence games, and has a great community happy to help beginners with teaching games and reviews if they ask.
www.tygem.com
www.wbaduk.com
pandanet-igs.com
www.gokgs.com
Have fun playing!