Good news, everyone! I was right!
Futurama begins with a ridiculous premise that sets the tone for the entire show: Philip J. Fry, hapless pizza delivery boy, delivers pizza to a cryogenics facility on the last day of the millennium and falls into a cryogenic pod, as you do. He wakes up a thousand years later and begins working for another delivery service, Planet Express. Fry is a dolt in the Homer Simpson mold, and, like Homer Simpson, he becomes implausibly dumb for the sake of a joke. But he's far more endearing, especially thanks to his enduring crush on Leela, the one-eyed captain of the ship, who thinks he's sweet but does not return his affections. Bender is a hard-drinking, violence-loving robot in the Homer Simpson mold, and, like Homer Simpson, he becomes implausibly cruel for the sake of a joke. But he's...not very endearing, really, though he has his occasional moments of sweetness that are quickly forgotten when he once again acts in complete self-interest. Amy Wong is so rich she doesn't understand money and so promiscuous she doesn't understand commitment. Hermes is a Jamaican accountant, the ultimate bureaucrat and limbo master. Professor Farnsworth gives the orders and performs all manner of mad science.
It is hilariously appropriate that I forgot Zoidberg, the crustacean alien doctor whom everyone hates except the audience because he is wonderful. His always pathetically sincere "Hooray!" has become my definitive conception of the exclamation.
Character development is not necessarily a concern for the show; pretty much everyone is fundamentally the same at the end as they were at the beginning, even though they've gone through a lot. Fry and Leela's relationship ebbs and flows, and Amy finds love for a while, but I think we get far more character development in backstory than we do in the present storylines, and those are quite fun! Since everyone's character traits and quirks are highly exaggerated, I enjoyed watching the writers attempt to justify them and give them real resonance.
While Futurama holds very little regard for the laws of physics, reality, and even general logic at times, there's no question it's a smartly written show, full to the brim with math and science in-jokes and veritably overflowing with puns ranging from groanworthy to incredibly clever. I was impressed with how many variations on characters' catchphrases they could come up with; who knew "Good news, everyone!" could be so versatile? Who knew there were so many different reasons Hermes could cry, "My manwich!"? How many things could Bender say are 40% something? Not to mention the many, many variations on "Bite my shiny metal ass." Although there isn't a huge amount of continuity, it's little things like these that reward the dedicated viewer. And the many recurring characters, be they as unimportant as the old lady who says "Kajigger" all the time or as plot-relevant as possibly my favorite recurring characters, the Robot Mafia (CLAMPS!). The show builds a huge universe—literally, the crew goes on adventures all over the damn universe—and it will bring back small elements as cameos or to play key roles (Nibbler and his race being one example).
It's hard to sum up 140 episodes of sci-fi humor in one post, so I thiiiiiiiiink I'm going to stop trying. There's far too much to talk about! So much creativity! So many memes! So much added to the cultural lexicon! It's a great body of work, highly entertaining, all the way to the end.