Boardspace.net is a noncommercial site devoted to realtime abstract
strategy games. If you think "chess server" you'd be right in all
respects except you've probably never heard of the actual games
I host.

Steadfast has hosted my site on a VPS for a year or so, and it has been
very satisfactory.

"Game Sever" includes a lot of different types of site, but I bet I"m
the odd one here.