There is only one answer to this question: Ragnarok Online.

You can say what you want about playing Counter Strike or whatever but sitting on my friend's private server hunting for items with my friends and then going into a massive War of Emp. match against three guilds was a blast. The fact that we were drinking the whole time and listening to HORRIBLE J-pop helped too.

And though this isn't really a LAN party, playing any of the following with friends is great too: Soul Calibur/2/3, Mark of the Wolves, Street Fighter III: 3rd Strike, King of Fighters 2003, and Guilty Gear XX #Reload.