The factions in Warhammer 40000 were originally little more than faction-level Expies for Warhammer Fantasy factions. Although they've tried to tone this down a bit -- for instance, by phasing out the Squats without explanation, then finally saying they were just eaten by the Tyranids -- there's still obvious parallels. Empire --> Imperium, High Elves --> Eldar, Dark Elves --> Dark Eldar, Undead --> Necrons, Chaos --> Chaos Space Marines, Greenskins --> Orkz, Dwarves --> Demiurg (a Tau-allied race), and to a lesser extent, the Tau in general. The Tyranids are an exception -- there's been some awkward attempts to equate them with the Lizardmen, but it doesn't really work out.
Especially since the Slann are more or less the Warhammer 40K equalient to the lizardmen, while the 'nids are more or less expies from Starship Troopers.
The Tyranids also draw somewhat on Alien, while the Tau look an awful lot like the Trade Federation from The Phantom Menace, both in terms of character design and vehicles.
An example of a smaller background race in the setting is the Hrud, who are practically expies of the Skaven in many ways. At least as far as the fluff regarding them gives away. Both are rat-like humanoids who live in sewers in various places, and both use warp-plasma based technology and are scavengers, plus the addition of similar social habits. It is highly unlikely that they will become any kind of major faction in the tabletop, however, since Games Workshop are heavily opposed to the idea of having Warhammer 40000 as simply Warhammer in space, due to the removal of the Squats, the original Dwarf expies.
As of its printing, Games Workshop has some funky canon out now that makes them look like weird spine-like jellyfish people (which is actuallyquite plausible when you...). Although they still have some Skaven elements (photophobia, cavedwelling, Warpstone usage), they also have some new canon junk like a God Pantheon, a curbstomped god who was shattered into psychic shadow spheres called Umbra via Slannesh (who else), and some weird time-distortion, warp-radiation field of narminess which they constantly radiate about themselves.
Also, the Imperial Arbitrators were recycled from an abandoned Judge Dredd tabletop game.
Nearly everything in W 40 K is an expy of something from another setting. Aliens vs Starship Troopers vs Colonial Marines vs Terminator vs Robotech vs Elves vs Orks vs Demons etc... While the original game was largely Warhammer Fantasy IN SPACE, the current iterations of W40k are closer to "sci-fi trope deathmatch" with the awesome and grimdark turned up to 11.
While being essentially the tomb lords from Warhammer Fantasy, the necrons are also clearly terminator expys. Rules like "I'll be back" are pretty obvious clues.
The tyranids are pretty clearly expys of both the Aliens and bugs from the Starship Troopers movies, depending upon the subsetting.
For example, genestealers and general indoor fighting of tyranids is heavily based on the Aliens film. Space Hulk was basically Aliens, the board game.
While the outdoors stuff, especially the perennial matchup of imperial guard vs tyranids is straight up Starship Troopers, the movie.
Don't even know where to begin with special characters and personalities from the fluff and the books. It's basically a flood of expys.
Here is one: Commander Farsight was a prominent leader of an Empire's military forces. He eventually led some of his brethren in a rebellion against the powerful ruling cast, who's whims most Tau serve their entire lives. He is also known as O'Shovah.
The Ravenloft game setting is swarming with Expy versions of classic characters from Gothic literature. Dracula, Dr. Frankenstein and his creation, Jekyll & Hyde, and so on: they're all there, sans serial numbers, disqualified from being Captain Ersatz only because the originals' copyrights all expired ages ago.
The Forgotten Realms setting of Dungeons and Dragons has a few also: King Azoun IV of Cormyr is pretty obviously King Arthur, especially with regard to the whole "Sleeping Sword" thing, which parallels Arthur's "Sleeping King" myth pretty well. Arthur's coat of arms was a golden dragon, Azoun's is a purple dragon, etc. Also, Yamun Khahan was a very obvious expy of Genghis Khan. So when the two of them fought in single combat....
It's implied that Chandra was taught by Jaya herself, going so far as mentioning Jaya's name when recalling one of her lessons.
Pokethulhu has many expies (often double-expies) of characters from both of its "parents": Randy Carter (Ash Ketchum/Randolph Carter), Derleth and Bloch of Team Eibon (Jessie and James of Team Rocket), and even Pikathulhu (Pikachu and Cthulhu).
One of the supplement books for Werewolf: The Forsaken, Skinchangers, has a character in it called Shuichi Kurama who is serving as a Host to a fox-spirit named Yoko. The manga/anime series Yu Yu Hakusho has a fox demon named Yoko Kurama who was mortally wounded and took refuge in the womb of a pregnant woman, Shiori Minamino, and was reborn as her son, Shuichi Minamino. On top of that, the physical descriptions and personalities for both Shuichi Kurama and Yoko Kurama are very, very similar.
In Strike Legion, just about everything is an expy of something from another sci-fi or fantasy setting. The game not only shamelessly rips off other settings, but then it takes those same things and turns them Up to Eleven.