Seconding Forbidden Island/Desert/Sky. Island is what I break out to introduce new folks to co-op gameplay, then switch to Desert once they get the hang of it.
Pandemic hits a lot of the same notes, and can get really hairy at the end.
I see the app as the DM. Plus, you can tell it what expansions you own, and it includes it all when it makes the map — you can play the same scenario and get different layouts.
One of my favorite Sims torture chambers housing projects was a spiral with espresso machines at each corner. In the middle was one toilet. I invited all of the neighbors over and watched the chaos unfold.