In Elder Scrolls: Oblivion, certain NPCs are programmed to travel to different cities on specific days of the year. You might encounter an NPC that you met in Chorrol drinking at a tavern in Bruma, or murdered by bandits on the road to Anvil.
Skyrim has a few cases of this as well (e.g Khajiit caravans), but to a much lesser extent than what is found in Oblivion.

To me it enhances the gameplay when done properly, with Oblivion being a good example. I can only speculate as to the reason. Perhaps it just makes it easier to imagine that you're visiting a real living game world when you play. Immersive seems like a fitting word then. In the very least it bugs me to no end that it's not the case in Morrowind, even though from a purely mechanical standpoint it's far more convenient.

Of course the degree to which this is important varies widely between players, as dtgreene could probably attest. I seem to recall dt frequently mentioning that immersion is of little importance. But for me it is often a big deal.

I care a lot about immersion too, but I don't always consider 'realism' to be the same as immersion. How about a game wherein you had to go poop twice a day? :-P

Like The Sims? :) This conjures images of having my sim drink cup after cup of espresso in the mornings before work, inevitably pissing his pants, just to have enough energy to get through the day. Though that completely backfired if he didn't get a chance to shower before the carpool showed up...

But yeah, I suppose it would be an interesting thing to research for somebody so inclined. At the end of the day it's still fantasy with the aim of having fun, so even if something adds to the realism, we only want to include it if it has a net positive effect on the fun. Which for an RPG might not be included by, uhm, those bodily functions...
But stuff like for example eating and drinking could be when done right. Something like what Mortius1 mentioned on the other hand, making it annoyingly difficult to find npcs, would be an example of not doing it right. In Oblivion at least you can ask other NPCs, like a guard, if they've seen so and so, or learn paterns eg: Mary like to go the market on weekdays.

In cinema they call this 'suspension of disbelief', or how the craziest most unrealistic stuff can still be very immersive. ;-)

But having to eat and drink can hurt a game if done wrong. Ultima 7 is one example of a game where you have to manually feed your party members, doing so requires interacting with the game's rather poor inventory system, and food is easy enough to come by that it doesn't really add any challenge to the gameplay; it just adds busywork. (Ultima 4-6 handled it better; in 4 and 5, you only have to buy food and don't need to worry about eating it, and Ultima 6 has food automatically consumed on rest (and you otherwise don't need to eat).)

Dungeon Master also requires manually feeding your characters, but you don't need to do it as often, and the game actually has a good inventory system, unlike Ultima 7. (There's still the issue that food/water aren't as important enough for the mechanic to warrant its existence, but at least it doesn't get in the way as much.)

The need to eat and drink would have made more sense in, say, a Dark Sun game, but the two accessible Dark Sun games don't actually implement that sort of thing. (The third Dark Sun game, Cimson Sands, is a defunct MMORPG that (to my knowledge) is not playable these days, so I don't know if it has this sort of mechanic.)

Exactly :) It would perhaps be very interesting if somebody approached this academically from the point of view of games where it's definitely present to some degree as well. It can be crazy and unrealistic like you said. Like Alley Cat of all things, which weirdly I think I kind of immerse myself in a bit each time I play. Though, perhaps I'm just confusing that with an intense nostalgia. Still, I'd love to be able to explore that kind of game world, with exactly that kind of graphics, only beyond the alley in which the game takes place. Same thing with something like the first Police Quest. OR perhaps I should just play less games ;)
Oh absolutely. I like Jagged Alliance 2's approach (1.13 at least, not sure if in base game) in this regard. The mercs eat automatically when needed if food is in their inventory, but you can also eat manually. The former you would typically rely on when you buy food in bulk, like MREs, and just stuff it into everyone's inventories. But the latter is useful as well, for example when visiting a town and ordering some steaks and pizzas from a pub. Then you can satiate everyone's hunger and preserve your cans of beans and so on. Same thing with drinks.

Food and drink works pretty well in an MMO setting as well, because any character can, independent of their class, compliment his/her usefulness to a party in a difficult encounter by distributing specially prepared food and drink. It's also a nice feeling standing in the kitchens and using your hard acquired skills to prepare food for such occasions.

It's not necessarily nostalgia. A game itself can be not very 'immersive', but you yourself were very immersed in the game when you played it.

As said by someone else Stardew valley, but Legends of zelda breath of the wild, they kinda do the same stuff everyday but it seems like they have lives.

... when you wait for an NPC to leave their home to burgle it undisturbed.

I do love the illusion of a living world (that moves on its own and is not dependent on the player) this creates, but of course a game like that should have some kind of waiting mechanic.
Likewise I simply love it when in the wilderness beasts like wolves prey on deer etc.

"Work fascinates me. I can sit and look at it for hours!" ;-)

In Hero-U, your fellow classmates have active lives... in addition to showing up to class with you, they can be found exploring the dungeons, hanging out in the practice room, the library etc. They have meals together, and can have romantic interests in each other.

Other RPG game like Kingdom Come deliverance, or Legend of Grimrock, Might and magic series