If you've seen The Sixth Sense, the final twist could've left you thinking over it long after the credits had run out. Like Brothers: Tale of Two Sons (Starbreeze Studios/505 Games, 2013) didn't leave me be after I had finished the game.
If you eat cotton candy, you might like it as you eat it, but once it's finished, it'll only leave you feeling hungry. Like when I turned off Legend of Zelda: Breath of the Wild (Nintendo, 2017) or Hyrule Warriors (Koei Tecmo, Team Ninja, Omega Force/Nintendo, 2014), they didn't stick in my mind despite pouring far too many hours into them.
Do you find most enjoyment of the game when you play them or after you've shut down the game?
Personally, I appreciate the latter more, and not in the snarky way.
I finished BotW after some 160 hours or so, probably sometime in April. Yeah, I played the game a lot... but after closing the game, it was like I had been eating some thin gruel. As I try to remember something about the game today, there's only small, unconnected clumps floating in the water.
Contrast that with Xenoblade Chronicles X (Monolith Soft/Nintendo, 2015), where I can remember the monk-style character. Not his name, though, just his attitude towards alien life. Or how I sneaked to plant a probe next to a sleeping giant six-limbed primate. Or the game's ending. Open endings are an easy way to make the game stick in your mind after you've played it... for better or for worse.
It's not just about the plot, though. I remember the time I flooded the entire valley in Dwarf Fortress (Tarn Adams/Bay 12 Games, 2006) drowning all the dwarves in the cave, and that happened probably back in 2007. Meanderbot's experience in Nethack (1987) where they fired a sleeping spell at a silver dragon that reflects magic might be as memorable. Emergent events can be that way.
Another way to enjoy games after closing them is to have the games feel like palate cleansers - taking the mind off of something and maybe raising that pulse in lieu of going for a run. A few rounds of an intensive action game (shmups in my case) and the game is forgotten as it is shut down, but the effects persist.
I'm tempted to say that long games have inherent problems in having value outside the time they're being played. The first times the player find Korok seeds lose their uniqueness once they've got some tens of them and they blend into a vague mental blob, consisting of just generic descriptions like "fill in the stone circle" or "place an apple on the empty tray".
Having a character in the team permanently die would lose its meaning if the character is only one of half a dozen characters that are lost over the story arc. Then again, at that point you'd remember the game just for killing so much of its cast.
I can't state that claim with confidence, though. Given what I've heard of Witcher 3 (CD Projekt RED, 2015), its sidequests are varied in plot and memorable despite the game being a lengthy one. Divinity: Original Sin 2 (Larian Studios, 2017), too. Not every RPG is like the copy-paste dungeons of some RPG I never played (Dragon Age something, I think). Would the battles against big monsters in Monster Hunter stop being separately identifiable? I can't, because I have found myself avoiding most such long games.
Far be it from me to say that people enjoy their games "a wrong way", but I've seen most arguments around game length revolve around how good the time spent playing the game is, and I think that line of reasoning is missing a fair bit of the enjoyment in the titles. There should be no reason why games can't do what the Director's Cut of Blade Runner (1982) did with leaving the viewers ask themselves who Deckard actually was.
(Of course, I admit I'm an odd one for feeling the main reason to watch movies is to be able to talk about them after it's over.)
So here's the question. Which games have you been stuck thinking about long after you've finished them and why?
(EDIT: Fixed CD Projekt's name)