First of all, many of the main characters are voiced by the same man, Billy West. He does the voices of Fry, Dr. Zoidberg, Professor Farnsworth and many other secondary characters. While that's fairly common in animated shows, what is unusual is that he will do all the voices all in one take instead of multiple takes. West is often voicing three or even four different characters in the same scene, all in one take, switching back and forth flawlessly!
Cubert Farnsworth, Professor Farnsworth's clone child, was always a planned character for the series, even though he wasn't introduced until the second season. In his first appearance, he essentially played an animated version of the fans who point out plot holes and other inconsistencies, which are rampant in the show. It didn't quite work out how the writers and producers planned, so they just turned his character into more of a normal boy after that.
Futurama was named after the exhibit of the same name at the 1939 World's Fair. Suprisingly, that wasn't the first name considered for the show. Earlier choices for a title were "Doomsville" and "Aloha, Mars!"
While you might know that Professor Farnsworth was named after Philo Farnsworth who was an inventor at the 1939 World's Fair for which the show is named, you probably don't know how the other characters got their names. Philip Fry was named after the late Phil Hartman who was set to play Zapp Branagan until he passed. Bender was named after John Bender from The Breakfast Club. Perhaps the most obscure naming was Turanga Leela who was named after French composer Olivier Messiaen's 1948 Turangalîla-Symphonie.
It looks like the creators of Futurama took the term foreshadowing a little too literally. At least two times they have inserted shadows of characters yet to be introduced into scenes way before we ever saw them in reality. In the very first episode, you can see a shadow of Nibbler under the desk when Fry falls into the freezer even though Nibbler doesn't show up for several more episodes. And later, we see Leela's parents in the background of a sewer scene a full two seasons before we meet them!
Everyone's probably wondered how Matt Groening came up with the idea for Futurama. The answer is that he came up with the idea while listening to a song called Robot Blues by a 60s psychadelic Scottish folk band called The Incredible String Band. If you go read the lyrics, you can practically hear Bender singing them!
While it might seem like Fry and Leela's outfits are plain and randomly chosen, they aren't. Leela's plain white tank top is supposed to look like Ripley's from Alien, and Fry's red jacket is modeled after James Dean's in Rebel without a Cause.
Fry's loyal dog Seymour, who waited around for his owner to return after he disappeared into the freezer and died outside the pizza place was actually loosely based on a true story. There was a dog named Hachiko who waited for 9 years for his owner to return after his death.
You know that hilarious image of 30th Century Fox that airs at the end of every episode? Well, it almost wasn't there. Fox actually was entirely opposed to the idea of it and only allowed it after Matt Groening bought the rights to it.
There is a full length episode, 22 minutes long, consisting of just the Hypnotoad. At the end you will hear a voice that says "the audience will wake up remembering nothing and feeling refreshed." The hypnotoad is extremely popular, even with people who aren't fans of the show and is one of Matt Groening's favorite characters as well.
Bender was made for bending of course, but his antenna is an often overlooked feature of his robot self. His antenna has had almost countless funtions over the years Futurama has been on the air including: a beer pump lever (of course), a timer button for his internal digital camera, a popcorn butter dispenser lever, a flusher, a pager vibrator, a snooze button, a cooking timer, a voice mail alert light, a voice mail delete all button, an audio tape dispenser button, and for sexy times.
You probably know that Al Gore, a big fan of Futurama, has voiced a few episodes as himself. You might not have known that his daughter Kristen Gore has actually written for 6 episodes of the show!
The alien language that is used in the background occasionally throughout the show has been changed twice so far because the very clever fans of the show keep figuring it out!
Futurama put out multiple feature length films in a short time, but you probably don't know what a feat that is! It usually takes about 4 years of work to make a movie length animated film, especially ones in HD, and they did 4 movies in 3 years! And they didn't skimp either. In fact, they got fined by the animation studio for having over 250 characters in one scene in one shot in Into The Wild Green Yonder.
In the episode where the cast switched bodies, the mathematical theorem shown for how to switch them back wasn't just random. The episode writer, Ken Keeler, who holds a PhD in Mathematics actually wrote a real theorem on how people could switch bodies.