These are local multiplayer games as opposed to just co-op games
Check out these sites for info about local multiplayer games:
http://store.steampowered.com/tag/en/Local Multiplayer/
http://store.steampowered.com/tag/en/Local Co-Op/
http://www.co-optimus.com/
http://pccouchcoop.com/
http://pcgamingwiki.com/wiki/List_of_Local_Multiplayer_Games
Due to the fact that fighting games need quick reactions, a lot of fighting game fans prefer to play face to face. See if there is a fighting games community in your area. Here is the Coli fighting games thread:
http://www.thecoli.com/threads/official-fgc-thread-streams-pop-offs-fukkery.230503/
If you have a 3DS or a Vita, most multiplayer games have an ad-hoc multiplayer option in addition to an online option. Some games only need one person to have a copy of the game.
Nintendo doesn't make online gaming a priority over local, so Wii U owners have lots of local games to play:
Super Mario 3D World -
http://www.thecoli.com/threads/super-mario-3d-world.152023/
Rayman Legends
Mario Kart 8 -
http://www.thecoli.com/threads/mario-kart-8.167376/
Pikmin 3
New Super Mario Bros. U
New Super Luigi U
Donkey Kong Country: Tropical Freeze -
http://www.thecoli.com/threads/donkey-kong-country-tropical-freeze.152957/
The Wonderful 101 -
http://www.thecoli.com/threads/the-wonderful-101.141630/
Nintendo Land
Sonic: Lost World -
http://www.thecoli.com/threads/sonic-lost-world-wii-u-3ds.120143/
Upcoming Wii U games:
Hyrule Warriors -
http://www.thecoli.com/threads/hyrule-warriors.221764/
Bayonetta 2 -
http://www.thecoli.com/threads/bayonetta-and-bayonetta-2-wii-u.140911/
Super Smash Bros. -
http://www.thecoli.com/threads/super-smash-bros-wii-u-3ds.121222/
Another good thing about the Wii U is that it is compatible with Wii controllers, so if you own a Wii, you already have extra controllers for other people.
This next list of games are PC games, although a lot of them have been released for other platforms. A good thing is you don't need a gaming PC to play a lot of these games, which means that if you have a relatively modern laptop with a HDMI out, you can play these games on a TV which solves the "huddling around a computer screen" problem.
Awesomenauts
Battleblock Theater
Castle Crashers
Hidden in Plain Sight
Jamestown
Lara Croft and the Guardian of Light
Monaco
Portal 2
Samurai Gunn
Sonic & All-Stars Racing Transformed
Sonic Adventure 2
Spelunky (Extremely fun in co-op.)
Towerfall Ascension (Also very fun) -
http://www.thecoli.com/threads/towerfall-ascension-linux-windows-mac-ps4-ouya.196529/
Trine
Trine 2
Many more that I can't think of off the top of my head