As FPs are being mentioned, Nothing beats good old doom. Play online doom games by downloading skulltag and zdaemon (needs original ddom files but there is a free file available that would do the job. Go to
www.skulltag.com and
www.zdaemon.org to get them. They come with launch programs (where you can choose games to play) but you can get one with other rooms by downloading player connector (
www.playerconnector.com) and it works with other famous games. most computers should be able to run all of these.