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In no particular order:
Online/LAN:
Xonotic: Good for online/LAN-play. UT-Style FPS.
OpenRA: Damn well good. RTS.
Warsow: Similar to Xonotic, but much faster. Damn good game. Sadly, defunct.
Sonic Robo Blast 2 Kart: If you like kart games and think they are all to easy, this is your choice.
Online/Split Screen/Couch coop:
SuperTuxKart: Damn fun, especially with a few add on tracks and good company at your place.
Hedgewars: Similar to Worms: Armageddon.
Battle for Wesnoth: Really fun once in a while. Neither the online nor the local experience is really "better".
Offline/Split Screen/Couch Coop:
Atomic Tanks: Worms on steroids.
Barbarian: Rocks. The OSS-Version is a tad bit obscure.
I didn't do VCMI, but Homm3 is one of my big local multiplayer favorites. I wait for the full inclusion of WoG before shooting it up. Also, as a young boi I really loved C-Dogs. The thing is now open source, check it out.
Most of Warsaws devs and players have moved to Warfork after disagreeing with the actions of Warsaws owner.
I used to play a lot of Warsaw and never heard of the fork. I'll Check it out later tonight, thanks!