Some of the most popular LAN party games are League of Legends, Team Fortress 2, Path of Exile, Alien Swarm and Left 4 Dead 2.
League of Legends is a popular MOBA game that is free to play. The game consists of two teams of five that fight on a traditional MOBA tower-based map. There is a jungle, and players fight against each other in lanes that are assisted by small minion units. There are also additional game modes with two teams of three or two teams of five in a circular-based, capture point style, dominion mode.
Team Fortress 2 is a free to play FPS game with cartoon flair. There are classes within the game that provide players with different play styles. There are many modes and maps. The Man vs. Machine mode is perfect for LAN parties.
Path of Exile is a free to play dungeon crawler with a huge amount of content and customization. It's easy to run and fun to play with friends. It can also be difficult.
Alien Swarm is a great co-op, top-down shooter game that relies on teamwork. It is free and the combat is fast paced and fun.
Left 4 Dead 2 isn't free, but the zombie infested world has a lot of maps for players at a LAN party to explore and live through in fast-paced arcade FPS style.