I am in a slightly better state/position than I was yesterday, so here is a more comprehensive response.
For me, nothing beats Skyrim. I think it's unlikely that anything will ever top it for me, even the next Elder Scrolls instalment; ESO was a shocking disappointment, and Bethesda need to really pull their finger out on whatever they do next. But Skyrim is the sole reason I still have my Xbox 360 set up and ready to go.
Fallout 4 was the first in the FO series I played. It's amazing, not too far behind Skyrim. Despite having it since it was released, I didn't even install it on my console until mid-January, when I was housebound for 2 weeks. I then played it religiously. But I like to just explore and do the side quests in the Bethesda games, so I'm still a long way off finishing the story. And I haven't even considered downloading the DLC yet.
I like The Division, but after playing it almost non-stop for 2 weeks, I got a little bored. I only like to play Co-Op with friends, and sadly none of mine bought the game, so I was playing it alone
It's a great game, but it is clearly made to be multiplayer, so on my own it just got a bit repetitive and boring... and difficult.
Battlefield 4 is amazing. When I get online with my friends we always have a great squad. We all enjoy playing our own particular roles, making us a diverse and effective unit. Unlike Call Of Duty *spits* Battlefield is all about the online matches (the single player campaign is short and a little weak), and they encourage team play while almost punishing those who play 'lone wolf.' It also requires more realistic and intelligent use of particular weapons (no running about with an LMG hosing everything, and no 360 no-scopes with a sniper rifle).
I still GTA 5, but having completed the single player story a couple of times, I just want to use the multiplayer. Unfortunately, I again just enjoy fucking around with friends rather than doing the races and deathmatches, and my friends are not online much these days. They also made it too money-orientated, meaning that having not played in a while, all the new stuff requires millions of in-game dollars which I can't be bothered to earn, so if I am to enjoy new content I would need to spend RL cash. Not worth it, so I won't be playing this until I have other people I can play it with.
Assassin's Creed - all of them, I guess. I only have Black Flag and Syndicate currently, though. I fucking love pirates, so Black Flag will always be one of my favourites. As for Syndicate, I really enjoy it - I suppose being English it feels a lot more like home than any of the others - but I haven't played it in a while, and am nowhere near completing the main story. I need to get back to it soon.
Fifa 16. I'm a football fan, and had I been a little more popular at school and less academically orientated, I may have been good enough to play at a semi-professional level. So Fifa games give me the chance to live out my 'dream' of being a professional footballer, or just attempt the unthinkable and take Burton Albion all the way to the Champions League final. This is probably the only game I don't have periods of not playing, but I haven't actually finished a season in Manager Mode on Fifa 16, and didn't on 15 either. And I normally play 2-3 seasons on a Pro career before just starting again. And I always say I won't get the next one, but I typically do.
I used to play Football Manager on the PC, but not since 2011, simply because the newer ones are way too memory and processor hungry, and I am not spending a fortune on a decent PC or laptop. If I do eventually spend the money on a gaming PC setup, then Football Manager will be one of the games I buy.
I liked Halo 3, I enjoyed ODST, and I loved Reach. Then I played 1 and 2, and they were fucking awesome. Halo 4, in my opinion, was dreadful. I didn't even bother with 5(?).
I won't argue with anybody about this, but CoD for me is shambolic. The early ones, yes, but after WoW they have been appalling. The stories get laboured, the Zombies got old pretty quick, and the multiplayer is overrun by 12 year old kids. If you want to see the difference, play Battlefield; CoD players can't play Battlefield, because they are too used to wandering off on their own, and they just get destroyed. But if a Battlefield player goes into a CoD match, they just own everybody, because they play tactically.
I can't think of any others I still play, or feel I need to mention, but I will add to this list if I remember any more.