There's lots of not-so-deep ones out there in the new "board games renaissance", too - like Forbidden Island / Forbidden Desert, Sheriff of Nottingham, or recently this year, Secret Hitler.
They take like 2 minutes to set up, 2 minutes to understand the rules, and are loads of fun even for kids (maybe not so much on the kids with the Hitler).
They take like 2 minutes to set up, 2 minutes to understand the rules, and are loads of fun even for kids (maybe not so much on the kids with the Hitler).