Ok, so no civilization games...
Are we talking about all time favorites? Ones you won't play anymore (won't enjoy if you did, because they're that old / unplayable no more / etc), but have good memories of and consider awesome, if not best for its time?
If so then hands down GTA: Vice City. That game was such a masterpiece. It was in the right time in the right place. That game spoke to my 13 years old soul like no other game
Another was TES: Oblivion. I was a late bloomer to that one. Got it on ps3 when it just released (ps3 I mean) and as we all know, there were no games for ps3 back then
I remember playing it that whole summer. It felt absolutely surreal. It felt like I could do anything in that vast amazing world. Oh how the times change... (I sticky FO3 and NV here to number 2 because I wouldn't want those game to dominate the list. Those are definitely part of number 2, it just wouldn't be fair, same if civ weren't excluded and would dominate at least 3 spots).
Other honorable mentions (since 5 was the requested number):
3. Dragon Age: Origins... Absolutely amazing and my first "proper" RPG. It went downhills from there IMO. DA2 and DAI were crap.
4. Mass Effect. It had a very interesting world, atmosphere, story, characters etc etc. It had massive potential. But as with DA I felt it went downhill with ME2. It felt like an interactive movie rather than an RPG game. They simply decided to not even try to make an RPG game and focused completely on story on characters. And it worked for many. Look how many people like it still. Never even tried ME3, no point whatsoever.
5. Surprising one, but CoD: World at War. I spent way too much time shooting nazis, commies, capitalist and um... Japs. Way too many hours trolling 14y-olds. Still think that the best FPS is a WWII FPS.
Now if we're talking about the recent ones, ones that I might or do play nowadays whenever it's not civ...
1. Skyrim. Obviously. Way too many hours there. Never once completed the main story.
2. Fallout 4. With survival/hardcore mode it's very much enjoyable. With alternate saving enabled that is.
3. GTA V I guess. I spend way too much hours online 1.5 - 2 years ago, mostly racing and focusing on vehicles in passive mod
Have to say that it has the most disgusting online community I ever encountered. Worde than any FPS teens by a margin.
Can't really think of two more sadly. I play games a lot, but I don't play a lot of games.