To draw this out more in detail in bulletpoints:
guards: private, public or unoffical? preventive, investigative or oppressive role?
murders, burglary, extortion and manhunts?
courts and vigilante justice? (just to add to this, I heard that in some Germanic countries the lord let his peasents have some sort of unofficial underground court system and that they took their responsibilities rather seriously, your thoughts on that?)
quests given to almost random strangers by a local lord? realistic?
grave robbing: Too rare to specifically look for them? thoughts?
elaborate india jones style traps?
adventurers? how rich, how poor? travelling into distant foreign land realistic? how big would the language barrier be and would translators be cheap and common enough to overcome that?
hostility of the natives, just prevent them from entering the city or kill on sight?
Rogues. Is there anything in the West that comes even close to the myth of the ninja? Whether it may be silently sneaking or wearing costumes and pretending to be someone else to gain entry to hidden places? And let's say at least trained, because I doubt there was demand for someone like that to be permanently employed?
Feel free to debunk other rpg tropes I failed to list here, these were just suggestions and all I can think of for now.
This might seem a little weird and pedantic, but it's kind of an important point: people today often read RPGs as taking place in an ill-defined, vaguely Tolkienesque late Antiquity, early Middle Ages.
But at the time D&D was being created (and if you look at the Original D&D Appendix N or the AD&D update you'll see what I mean - these are explored much more in depth here, in this Tor reading series), Tolkien was only one thread of influence, and really kind of minor at that. There's an awful lot more taken from two separate strands of pulp fiction: Robert E. Howard-style "Hyborian Age" adventures, and Jack Vance-style "Dying Earth" weird tales.
The Hyborian Age was a setting used by plenty of other authors, like Clark Ashton Smith and Michael Moorcock: It's a pre-biblical, post-Atlantean era based largely on Theosophical ideas about a globe-spanning Atlantean civilization that collapsed, with maybe a little 1920s-era speculative anthropology tossed into the mix. So way, way before the post-Roman "Dark Ages" and literally prehistoric. You can read Howard's narrative timeline if you like - it starts 20,000 years ago.
The Dying Earth hasn't happened yet - it's set in an equally distant future, long after some other undefined set of cataclysms in which whatever remnants of 20th century technology that still exist are utterly unrecognizable, and other branches of science have developed to the point of being indistinguishable from magic. Clark Ashton Smith, Andre Norton and Fred Saberhagen also wrote using this as a setting, and it kind of smudges nicely into far-future science fiction (so Asimov's Foundation books would slide in here kinda sorta).
The town guards, vigilante justice and quests-for-hire are really important tropes for Howard's stories, while elaborate traps and far-voyaging travelers (with language issues) are big parts of what makes Vance stories go.
Neither are really meant to be within history, really, even fictionally.
I'd be interested to see which tropes could be historically located, though, or how they'd play out in whatever historical setting.
First it's really important to understand that in the context of many RPGs, a lot of the things you are describing are really just abstract elements of Storytelling rather than a practical insert.
The legion of city guards you have to kill while on your way to assassinate a target in Assassin's Creed do not represent a facsimile of Jerusalem at the time - the guards are partly a pacing mechanism to take up your time, and an abstract representation of "difficulty" for the player to overcome. They are not real, because the game is not trying to truthfully re-create history, it is trying to entertain you.
However, they do take their inspiration from elements of the past. For example, grave robbing.
This has been an extremely prevalent problem for centuries on end all over the world. Merovingian tombs, tombs of Pharoahs, the list goes on and on and it has frustrated and stymied the work of scholars and archeologists practically since time immemorial.
There are an absolute wealth of resources about the practice of grave robbing, especially of Merovingian Europe, as a way to either gain wealth, or to damage the prestige and honor of the dead and their descendants.
Is there a specific instance you want to test any of these references against?
grave robbing: Too rare to specifically look for them? thoughts?
There is actually an episode in Grettir's Saga, generally considered among the best, in which the "hero" goes down into a tomb and loots it, and is confronted by the "spirit" of the tomb (in Norse mythology, "ghosts" were bodied).
hostility of the natives, just prevent them from entering the city or kill on sight?
Naturally this will vary a great deal, but there were parts of Song Dynasty Sichuan that were like this. There is an account of a new government official who said he could almost feel the eyes of the "natives" on him as he sailed down the river to Luzhou. Although in practical terms a city that is actually in open warfare with its hinterland will not last long.