Now this is an interesting question. There are only a few gaming experiences left that I really enjoy these days.
I love objective based teamplay games that play like 'sports'. If I had an XBONE I'd definitely be playing SMITE right now, but here are those kinds of games that turn my crank:
Tribes Ascend Home
https://www.dungeondefenders.com/2/
ROCKET LEAGUE - Coming July 7, 2015
I like fast, frenetic, twitchy combat/gameplay. I love to strategize, plan, coordinate with teammates, and manage resources. I love high skill ceilings.
I hate stealth mechanics, cover shooters, and 90% of platformers. Super Meatboy was alright. I got over fighting games in the 90s.
I don't give a shit about 'story'. Even The Witcher 3, a game that is getting heaps of praise piled onto it, I find underwhelming. I read a lot, and the stories game developers tell are just always sub par. I'm the guy that couldn't get through The Last of Us. I've never played through an Assassin's Creed, BioShock, or Mass Effect title. I'm a fan of brawlers - Bayonetta 2, DMC, and God of War come to mind. I love a fast paced racer in the vein of F-Zero, too. I love arcade style 'stunt' games like Tony Hawk or SSX, or any game with interesting movement.
All that being said, I know most of what I discussed isn't going to be present in an MMORPG, which is my favourite genre... The thing that most RPGs lack that all the games above have in common? Excitement.
I can only remember two MMORPG experiences that actually excited me, and they did it in two ways. In EverQuest, it was generated via fear (of death, progression loss), and in World of Warcraft it was generated by awe (encounter design, environments). In addition to fear & awe, I want meaningful economic/bartering player interaction, interpersonal reliance, and freedom. I have thoughts on how to achieve these things, but that would require a more detailed discussion.