Well all time favourite has to be Borderlands just because of the sheer amount of content, though you can't play Co-op on PC in the Borderland series, only console (massive letdown IMO). The real problem with most local co-op games is they tend to be like playing reskinned dungeon crawlers, so not a lot of the games are great per se, but there are a few good options depending on what you're looking for. I do wish companies put more time into developing co-op games that actually use the features of being co-op, because if I'm honest I have to say the thing we like most about co-op is just the communication and playing together.

Stardew valley is amazing to play co-op, but no splitscreen you need to do it over online and it's still in beta, I wish there were more options for splitscreen farming/building sims. Don't Starve Together is somewhat in this niche too.

For Dungeon Crawlers that are silly, Castle Crashers is one of the most fun to play together.

Puzzles, Portal 2 has it nailed (though sadly you cannot play the campaign together, a separate, well fleshed out, co-op section).

BattleBlock Theater is also a pretty dark humour fun puzzle platformer game to play together.

For platforming Guacamelee is amazing, it has it all, fun, cuteness, style and it's a pretty difficult platformer too. We've played this together A LOT. I would say don't try too much too early, you get powers later that make things easier, but first time we played we didn't know and did a bunch of really hard platforming that was clearly meant for later.

A nice kids games for platforming is Never Alone, it's pretty, puzzle platforming that also teaches about Native culture.

Rayman Legends is also a fun one for kids, or partners who don't mind kiddy games.

I feel like local co-op games could really use more farming and RPG games to play along with. Honestly, I'd rather a 'tether' style mechanic than splitscreen, when we play co-op we never go far apart anyway, it's part of teamwork. Sorry for the long reply!