in related news, i have pre ordered a copy of MGS V , which is getting very good reviews, something rare if compared to the past couple of entries in the franchise.
people are saying that for once the game is subtle in its storytelling and that its complexity is justified.
Sibling reordered MGSV yesterday, got bundled with Ground Zeroes. So good. Though I must say all the main entries have been very well recieved and the series wouldn't be what it is without its trademark convoluted insanity. MGSV does however appear to be tonally different and more subtle- but still has the typical zaniness.
Minecraft? (Haven't played it)
I can attest to this. The appeal of digital lego is very strong and it truly was a cultural phenomenon in the gaming world. I played it for a brief and intense period during 2010. I was not clever enough to make computers and calculators in the game so I stuck with making pretty buildings and little artifical ecosystems. This game made me feel like I had truly wasted my life- there was a point where I was like 'what the hell am I doing right now?'- even moreso than The Sims. While I've still been playing games over the following years, I think I stopped regularly gaming because of Minecraft.
Anyway, LoL, Minecraft and now DOTA 2 are all fitting answers. Starcraft 2 was pehaps expected to stand alongside these games but I'm not sure if it really matched the popularity of the others or its predecessor.
I guess the MOBA replaced the RTS and MMORPG.
And there's those usual entry-based (?) favourites like GTA, COD (FPS as mentioned above) etc
Skyrim had the world in its grasp for quite a while too. I think that works too.
Another very curious game (which I haven't played) is EVE Online, which is fascinating from the outside but up close it looks like sheer drudgery. Reasonably popular, totally and utterly life-consuming, very complex.
EDIT:
You said major but how about those smaller web and phone games like Farmville and Flappybird? Those were odd/popular/often unpleasant.