As Dwarf Fortress takes shape, the worlds that are genned by the game are becoming more and more defined in terms of culture, fauna, etc. I haven't really looked into the question very carefully (and I have not tried to ask the devs), but to me the DF fantasy setting, like the vast majority of fantasy RPG-related settings is heavily influenced by works of the three fantasy authors listed in the title of this thread (J.R.R. Tolkein [1892-1973], Jack Vance [1916- ], and Robert E Howard [1906-1936]). This is only natural when you consider that these three veins of fantasy had a huge effect on the original 1st ed AD&D meta-setting that is described by the early rule books and in particular the Monster Manual and DM guide, which in turn has had a direct effect on the vast majority of fantasy computer roleplaying games.
In any case, only the game designers have a real handle on what extent these authors or others influenced DF, and even they might not really know for sure the extent of such influence. However, we CAN talk about what the worlds created by dwarf fortress reminds us of most. As for my own impressions, here is why DF seems to resemble the works of these authors the most to me:
1) Tolkein: This one is pretty obvious; the earliest versions of DF were basically a simulation of a dwarf settlement as described in Lord of the Rings, in particular the history of the Mines of Moria. As with Moria, a dwarven settlement in the early DF versions would eventually (if the player insists on mining deep enough) be overrun by a demon freed from an infernal prison, and as the game has evolved this has mechanic been ingeniously preserved in a less scripted fashion. Tolkein of course adapted dwarves from pagan Germanic folklore and made them into the “short, sturdy creature{s} fond of drink and industry” that we have in this game, made subterranean-dwelling goblins their enemies, defined elves as willowy nature-loving humanoids, and so on. So in so far as DF is about dwarves, elves, humans and goblins, and has kept to its high-fantasy roots, the Tolkein influence is a no-brainer.
2) Jack Vance’s The Dying Earth (and perhaps other settings): A lot of people know that the magic system used in AD&D from 1st ed. on was largely inspired by the way magic works in Vance’s The Dying Earth setting. However, we don’t have a lot of magic in the game yet. Also, unlike TDE, Dwarf Fortress worlds are not planets orbiting a dying red sun that have hosted human civilization for millions of years and have accreted all kinds of technological flotsam and jetsam (what we would recognize as science fiction elements) over the millennia. So why does the game remind me of DTE? The main reason is because of the weird and nonsensical cultures, historical figures, religions, cults and so on that are conjured up by the RNG and placed in the typical DF world. TDE is characterized by humorously idiosyncratic and cloistered cultures that have little contact with one another, and are separated by large dangerous wastes filled with nasty creatures. In fact, the nasty creatures are another important point of influence… the ubiquitous boogey-men of DF are very similar to TDE creatures such as erbs, grues, leucomorphs, etc. that make it impossible to travel alone with any degree of safety, and the beastmen, forgotten beasts and their ilk in DF also seem to me to echo the endless menagerie of TDE creatures.
As a side note, I should also mention Michael Shea’s Nifft the Lean and it’s sequels, which is heavily inspired by Jack Vance’s Dying Earth setting (Shea actually wrote a book that was meant to be a sequel to the first TDE novel Eyes of the Overworld, but it was later supplanted by Vance’s own Cudgel’s Saga and thus wiped from the canon). The Nifft books might be described up as a melding of Robert E Howard’s fighting-man adventure plots with a Dying Earth setting. The main thing about DF that reminds me of NTL is the prominence of hell (“demon sub-worlds” in NTL) in both settings; in the novella “Fishing in the Demon Sea” ( found in NTL) a couple of adventurers are forced to crash through a hellmouth and search for a young prince in the demon sub-world filled to the brim with monstrous creatures that prey on each other ceaselessly. Interestingly enough, their entrance into the demon sub-world in this novella is accomplished via a runaway mine-cart that they launch into a swamp, so when I read about the latest dev log entries involving mine-cart physics (especially parabolic curve flying carts) I can’t help but wonder if the devs were thinking of this story.
3) Robert E Howard: It’s pretty straight forward; pretty much any setting that fuses pulp-action heroes with fantasy is probably influenced to some degree by Howard’s fantasy stories, and DF is full of swaggering fighting-men who boast and fight, fight and boast etc. etc. The civilizations in Howard’s Conan stories are based more on the ancient world rather than the medieval world, and the same is true about Dwarf Fortress human civs, for many of the same reasons- they tend to feature strongmen warlords, no central religion, distinctive costumes and physical racial types, and so on. I suppose also that the inclusion of evil creatures from the eldritch depths that sometimes take over and rule civlizations, as well as necromancers and the savage creatures that dot the landscape also remind me of Howard’s sword and sorcery fantasy stories. It’s hard to say what the DF world setting will look like after another handful of major development cycles, but I wouldn’t be surprised if it resembles Howard’s settings more as things move forward.
Anyway, these are just my impressions and I am not trying to pretend I know exactly what influenced the development of DF, nor what is going on in the minds of the developers.