Driving: GT Sport for me (much to even my surprise!) - severely lacking at launch, but I find the monthly additions of cars and tracks keep me constantly engaged and stop me getting to my long list of shame. 4 or 5 new cars to try out each month perfectly suits my available gameplay time.
Runner up: The Crew (first one). Hundreds of hours exploring, plus having driven US66 in real life just beforehand, it felt like I was continuing that personal adventure on my PS4.
Honourable mentions for Dirt Rally and, being sneaky but it qualifies, Burnout Paradise Remastered
Action/Adventure: I wanted to put Uncharted 2 here, but apparently that was released October 2009
so it's got to be Uncharted 4 instead. The perfect conclusion to the perfect franchise.
The Last Of Us just doesn't have that Uncharted sense of fun for obvious reasons so loses out. I play games to enjoy myself, not to get depressed!
This part of the list is limited as I spend much less time gaming now than i did in the 2000s and most of that time is spent on driving games. There are many more that would probably appear on this list as runners up if and when I get to them (God of War etc) but they won't surpass U4 in my mind.
Open World: GTAV (the wonderful offline campaign only) , unfortunately my attempt to play online just involved me being bombed/shot/blown up by others which very quickly grew tiresome...
Runners up are probably all still on my to do list (!) and mentioned above in this thread...
RPG: I tend towards JRPGs so, the first Ni No Kuni wins here. (Dragon Quest 8 won this for me in 2000s).
Runners up: Skyrim (shock horror
), a Yakuza game but not sure which one is the best(!) - probably number 6 as the conclusion of the story.
Dragon Quest 11 and RDR2 and Ni No Kuni 2 are potential candidates for the list too when I get to spend proper time with them, as are The Witcher 3, Judgement, Kingdom Hearts III, Assassins Creed Origins
In terms of which genre has been best served in the 2010s, it's hard for me to think of anything other than RPGs, for the sheer variety and depth, even if many are sequels or borrow ideas from elsewhere.