Wizard of Wor - C-64 , simple vusuals but great atmosfere and sound of desintegrator guns killing with friend all kinda dinosaurs and dragons is great fun.
Bubble Booble - any platform.
Golden Axe/King of Dragons,Double Dragon/Legend games - any platform.
Need for speed 4 - PS1 , utimate perfection of smooth dual driving games in my opinion.
Vigilante V8 and V8-2 games - PS1 and Twisted Metal.
Baldurs Gate dark Alliance 1/2 and Champions od Norrath 1/2 - PS2 - best hack and slash games for 2 players.
Navy Field - mobile naval warfare free to play(nearly no pay to win possibility here) game , has lots of ingame battle mods, but my favorite is to gather few friends in their best ships and go play Raid(battle vs vastly superior but mostly dumb CPU ships).