Futurama season 1 is by far the shortest with only 13 episodes.
1) Space Pilot 3000
The pilot episode. Fry goes to a cryogenics lab to deliver a pizza and ends up in suspended animation. He wakes up 1000 years later to meet Leela then Bender then Prof. Farnsworth.
-Dick Clark and Leonard Nimoy have cameos.
2) The Series Has Landed
We are introduced to the rest of the Planet Express crew, and Leela is pronounced captain. Fry goes to the moon for the first time but wants to see the real thing not the amusement park. Bender hooks up with a farmer's daughter and has to run from the shotgun-toting maniac.
3) I Roommate
Fry has been living at the company's HQ, and everyone is sick of him so he moves in with Bender. The little closet-sized robot habitat is too small for a human. They attempt to find another apartment together, but it doesn't go well.
4) Love's Labors Lost In Space
Zapp, Kif, and Nibbler are introduced. The Planet Express crew is going to a planet on the verge of implosion in order to save the animals. They are detained by Zapp who doesn't want them interfering with the natural course of the planet. Out of pity for the idiot, Leela sleeps with Zapp (which Bender and Zapp reminder her of many times in future episodes) allowing them to get away. They find themselves trapped on the planet which is on the verge of collapse, and the only salvation is for Leela to swallow her pride and crawl back to Zapp for another round of sickening lovemaking.
5) Fear Of A Bot Planet
The crew goes to a robot planet where humans are killed on sight. It's up to Bender to make the delivery, but when the robots find out he works for humans, they take him captive. It's up to Fry and Leela to rescue him, but they're in for a few surprises.
6) A Fishful Of Dollars
Mom and her sons are introduced. Fry finds out he's rich and becomes obsessed with things from his time period, especially anchovies (which are now extinct). Mom thinks he's a business mastermind who must be destroyed.
-Pamela Anderson guest stars.
7) My 3 Suns
Fry drinks the ruler of a planet inhabited by liquid beings. It is their custom to crown the conqueror king. Once crowned Fry will rule until assassinated which makes Leela uneasy. When the former king communicates that he's still alive in Fry's stomach, it's up to Fry's friends to find a way to separate them without harming Fry before the monarch's subjects use more violent methods.
8) A Big Piece Of Garbage
Years in the past New York shot a huge ball of garbage into space because they couldn't think of anything else to do with it. Now it's coming back to smash them into a little gooey mess. Citizens of New New York have been recycling for so long they don't grasp the concept of littering. It's up to Fry to teach these people to be messy so they can create a second ball of garbage large enough to deflect the first.
9) Hell Is Other Robots
Bender turns religious and drives everyone crazy. They tempt him to sin, and the robot Devil drags him to Robot Hell. Feeling responsible Fry and Leela quest to rescue him and enter a fiddle playing contest with a fiddle of gold against Bender's soul.
-Dan Castellaneta, voice of Homer Simpsons, guest stars. 2/3 of the Beastie Boys group have small roles and sing. There's a clever musical number in it by the regular cast.
10) A Flight To Remember
Largely a Titanic parody. Zapp pilots the 3000 version of the Titanic into a black hole. During the journey Bender falls in love with a well-to-do fembot. Fry gets caught in a love triangle as Leela pretends to be dating him to get Zapp off her back, and Amy pretends to date him so her parents will leave her alone.
-This episode sets up Amy and Kif's future relationship.
11) Mars University
Partially an Animal House parody. Fry enrolls in college, Bender helps the Mars U chapter of his frat to become cool, and Farnsworth creates a super-genius monkey that attends class with Fry. Fry and the monkey do not get along because Fry is jealous. Farnsworth insists that they work it out, but neither can resist taking a shot at the other.
12) When Aliens Attack
When the final episode of a TV show doesn't get broadcast in the 90's, what harm could it do? If a rough bunch of aliens 1000 years later are intercepting the signal to watch the show, and get majorly hacked off that they can't see the end of that episode, you may have a problem. L'rrr and his crew come blasting to Earth demanding to see the episode. Since Fry is the only person with any knowledge of the show it's up to him and cohorts to recreate the episode to the satisfaction of the attacking Omicronians.
13) Fry And The Slurm Factory
Mostly a Willy Wonka and the Chocolate Factory parody with a Spuds McKenzie spoof thrown in. Fry, who is addicted to Slurm wins a trip to the Slurm factory and gets to take everyone with him. They learn a terrible secret about Slurm, and party icon Slurms McKenzie shows his true colors.