NFS, Half-life, Killing Floor. Highly suggest Killing Floor, I had fun times with my friends when I was a teenager
Warcraft 3, Read Alert 2 (inc Yuri Revenge), Command & Conquer: Generals Zero Hours, Company of Heroes : Opposing Front (Inc Tales of Valor), H.A.W.X 2
By local, do you mean you could get 4 people on a couch playing on the same device? Super Smash Bros and Mario Kart are the only ones I can think of... You may want to look into board games, instead...? Here are some I used to play. Settlers of Catan 7 Wonders Race for the Galaxy
Super Smash Bros, Monster Hunter (Best) Dota 2 ? CS-GO Downhill 2 domination with ps2 emulator ! Minecraft FTB (not vanilla, vanilla is boring) Serious Sam series Board game perhaps? offline game is fun at times
Age of Empires, Warcraft 3 & Frozen Throne Expansion, Starcraft, Age of Mythology & Titans Expansion, SAS 4 (browser - zombies), and Diablo I (never played multiplayer, because I never had friends to play with me, but there should be a way to play with friends, right?) And, just saying, but I don't know what is Local Multiplayer Games - since I always played alone t-t - so I just said the ones that I remember that there was a way or another to play multiplayer.
Hero Siege One Piece Pirate Warriors 3 (Any Game In The Series Works) Naruto Shippuden Ultimate Ninja Storm 3 Full Burst (Recommend 4 more though) Pacman 256
Civ games... The also have hot seat, so everyone doesn't bees to have PC. One thing that I didn't see casually, is mention of tabletop games. Create stories of epicness together. Think D&d 5th Ed; warhammer or variants; shadow run; all you would need for each player is mic/speakers or headsets, with something like Skype.