Syndicate -- can be soloed and done cooperatively. Skill-based shooting with a good progression system that lets you upgrade weapons, special abilities, and your core agent all separately to your preferred playstyle. Also some of the best sound design for weapons I've ever seen (the sniper rifle in particular). Warhammer: Space Marine -- brawling and shooting perfectly mixed, with free-form tactics necesary to survive.
Well, in this case I would say Portal 2, Realm of the Mad God ( F2P), Trine, Synergy for Half Life 2 ( mod), House of the Dead 1&2 ( its a bit tricky to make coop in the second one pc version but I assume it is possible), Killing Floor, Terraria. I dont really like MMORPG-s but if you are a fan of this genre of game, I could suggest Dota 2 oor Silkroad, I used to play with this game a lot and I really enjoyed it ^^. If theres any other game I could suggest, let me know