Virtual Network Computing (VNC) can be used to access your computer from anywhere if it's connected to the Internet and you know its IP address (use ifconfig). vnc-java can automatically create a webpage with a Java applet that eliminates the need for a VNC client. Try using x11-vnc
for remote X you can also use simply X with xhost as X is a network protocol, or you can do X forwarding with ssh.
WINE will often run your old Windows programs very well. It's hit and miss, but often more complex, graphics-heavy applications will work better than specifically integrated Windows apps.
There are a number of unique, nicely-made open source games that run under Linux: