In the Looney Tunes cartoon Rabbit Hood (1949), when Bugs Bunny assaults Little John, who has been announcing Robin's arrival throughout the cartoon, with a vehement "Well, where is he?" his question is answered with an actual clip from The Adventures of Robin Hood (Errol Flynn received a personal copy of this short as compensation for the use of his image).
The Looney Tunes short Robin Hood Daffy (1958) mocks both Robin's swinging on a vine ("Yoicks, and away!") and his overly jolly laughter after being trounced and dunked by an opponent.
In the 1982 film My Favorite Year, Errol Flynnavatar Alan Swann (Peter O'Toole) stumbles drunkenly into a projection-room where one of his old films is playing: the actors dueling therein are costumed exactly like Robin and Sir Guy in The Adventures of Robin Hood.
According to Ben Burtt, the sounds of the laser blasters in Star Wars are modelled after the sounds of the arrow shots.
In the ALFTales cartoon version of the Robin Hood story (1988), the Merry Men spring off obvious trampolines during the attack on the treasure caravan (as they do in this film), and Gordon/Robin, painting a self-portrait, paints out what is obviously Errol Flynn's face and substitutes his own.
The Star Trek: The Next Generation episode "Qpid" (1991) is pretty much a Whole Plot Reference, down to a fight between Robin/Picard and Guy of Gisborne on a staircase—which makes Vash's absolute refusal to play Marian a whole lot funnier. (Oddly, though, someone somewhere seems to have gotten Guy of Gisbourne and the Sheriff confused, because Q is clearly playing Basil Rathbone-Guy but calls himself the Sheriff, and Guy more resembles the dim-witted, rotund Melville-Cooper-Sheriff.)
Robin Hood: Men in Tights (1993) obviously takes a few shots, but most notable is Robin's grand entrance into Nottingham Castle's hall, with a deer taken from the King's forests draped over his shoulders (though Mel Brooks switches it to a boar so that Robin can compare it with Prince John).
In The Simpsons episode "Take My Wife, Sleaze", Homer's motorcycle sword fight with Meathook parodies the ending sword fight between Robin and Guy of Gisbourne.
A fragment of one of the film's sword fighting scenes was converted to sprites by Jordan Mechner and used for Prince of Persia.