More typically co-op, besides seconding Squiz’s recommendation of Trine 1 & 2, Chariot has also been spoken highly of, and Cook, Serve, Delicious! has non-competitive play modes. I had a ton of fun with it in single player with a controller, very tactile game-play.
Another game that I really loved is Brothers - A Tale of Two Sons. I don’t remember it having co-op, but Steam begs to differ.
vinraith wouldn’t miss the chance to mention Lara Croft and the Guardian of Light. edit: another forum favorite that however leaves me completely cold is Sonic All Stars Racing Transformed.
**Screencheat **is technically competitive, but slightly reminiscent of hide and seek.
Not sure how fitting, other highly-rated games with local co-op that come to mind are Crypt of the Necrodancer, Towerfall Ascension, and …damn it slipped my mind.
Lorenzo Stanco’s useful tool reminds me of the following games, you can use it too, to find what you already have in your library and may have forgotten about.
Badland, Beat Hazard, DeathSpank, Guacamelee, Hammerwatch, Insanely Twisted Shadow Planet, Jamestown, Magicka, Mercenary Kings, Monaco, Pid, Portal 2, Rocketbirds (this is often recommended for the co-op by Heliocentric), Shatter, Slam Bolt Scrappers, The Cave, Broforce/The Expendabros (the latter is free), Tobe’s Vertical Adventure, Vertical Drop Heroes, Victor Vran, and Wyv & Keep.
^ just paste a link to your profile (public), then click on the Local Co-op tag.