May I suggest the following host...http://www.itanets.com
$60 (US) per year - that's only $5 per month
10GB Transfer per month
Plus a bunch of other features which you may or may not care about...(like PERL, C++, TCL, Python, PHP4)http://itanets.com/?a=hosting
I currently have 3 separate accounts with them for 3 different domains. In my experience, their tech support is top notch (very skilled in everything they do), their response time is measured in minutes (under 5 minutes).
I checked their terms of service and here is what they DO NOT allow...
# Copyrighted material
# Material that is threatening or obscene
# Material that is 'adult only content' or also classified as pornographic *
# Material protected by trade secrets and other statue
# WAREZ Software or not licensed MP3 files
# Spamming software
I'd bet if you sent an email asking them about using your server space for a game, they'd be okay with it as long as you promised not to break anything too badly.
Highly recommend these people, really. Also, you have to explicitly ask them to turn on certain features of their hosting, such as JSP/Servlet support, because not a lot of their customers actually want to use it.