Online gaming using modems or subscription services like TEN or
E-on will cost you money but you should at least enjoy the solidity
of a dedicated gaming network.
For the more technically savvy games can be played across the Internet without any service in between. One protocol you can use is the Internet Head to Head Daemon (IHHD). The name betrays its UNIX origins and you are going to need to be pretty sussed to set it up, as well as access to a UNIX shell account.
Easier is Kali shareware which tricks your PC into thinking that the TCP/IP protocols are actually IPX as found on many office networks. To find out more check out http://www.kali.com.
But as Internet Gaming goes mainstream with dedicated channels and networks being set up the need to set up such protocols will decline except among a dedicated hard core. At the recent E3 computer games trade show in Los Angeles, nearly every single exhibitor was announcing plans for online, and Internet connectivity.