I'm not sure if i can or even should classify all of these games in one category. But I'll try at least to sort them by games i play online and ones I play on my own.
It's mostly because in mmo/ online games I'm looking for totally different things than I'm looking for in games "offline"
In myltiplayer games I'm looking forward numbers! Yes, statistics, goals, achievements- everything that shows me how well I can play the game and what I should do better in competition with other players. So pretty much I'm playing games only for competition and raising different statistics by every 0.000% i can, to see how far i went from the beginning of my playing, up to this moment and trying to predict how far i can sill aim, giving my best to do so. Other interested thing I'm looking forward in specific games is trading possibility.
Online: 1) World of Tanks- My second most played game online. I've really comitted myself to this title, playing on different accounts sadly, playing really hard at some point. Always doing it with team of my best friends, with whom i've went through many clan, tournaments, ESL leagues and more. Such playing sadly tires a man more than many jobs would do. That's why now I'm no longer playing this title at all, because several games a week or even less it's hard to call playing anymore. Anyway, WoT and it's developer- Wargaming showed me for the first time how well the game developing might go on and on,for so many years and through all the criticism the title gets from people who mostly simply don't understand simple mechanics.
2) Diablo 2- Game i played for 11 years and it was probably my first multiplayer game i've commited myself to this level. This game was perfect, both as single and multiplayer. Here for the first time i started looking for any numbers i can raise in my stats/ items stats, as well as i enjoyed trading with other players for the first time. And since then I'm looking for it in pretty much every other game.
3) Wurm Online- This game is different than all other on my list. Well... i guess you all know this game good enough to see it. Honestly i don't know what holds me in this game for so long, but something certainly is...
4) Smite- In short, the only moba I could ever play for more than 15 minutes. And damn, I played it for like 2 years what in case of such kind of game for me- is a very long time.
In offline games I'm looking on other hand for something else. I rather prefer great stories that i can see, that i can hear and actively enjoy. Sometimes as already named hero with made history- or as a character i can create and make it's history by my own decisions. Character that allows me to feel like I'd be a part of great story myself.
1) The Elder Scrolls- as whole series. 2) Gothic- 1, 2 and 3.
3) Total War- as almost whole series, but especially Warhammer titles.
4) Life is Strange
5) The Walking Dead
6) Diablo 1& 2
7) Mount & Blade
Other games that doesn't fit at all to neither category are: 1) FSX- with all necessarry paid additions to make it a real simulation. (Basic Flight Simulator has nothing from simulation). As someone who loves flying, as someone who had a chance to fly on his own and pass basic trainings - i just have to love this title. That's why i have over 2500h "in air" on my beloved B734 and B738- 739 with over 800 hours in virtual airlines within. Pretty much every now and then I'm taking free day just to plan and go through next travel with my VR gear and bought or made B737 peripherals. Sadly, it takes a lot of place and time to set up properly, so i can't do that as often as i would love to.
2) NewZ- Once called WarZ, then Infestation... so poor game. Bugged as hell, plagued by cheates as hell... Sometimes it's impossible to play this title. however after all these years, finaly another developer who took this title under his wings made something decent out of it. Game has nothing to offer at all, but hell, PvP is so addicting in this game. Regardless of all bugs and glitches, PvP in this game is fast, so intentious and so rewarding and frustrating at once that i simply can't stop it, regardless of how much i hate this game. Sending a bullet through someone's head just to loot his precious corpse after that makes me wanna run this terrible game even now.