Plenty has already been said about the main characters and the music in other writeups, so here's my contribution of things not yet mentioned:
Cowboy Bebop is set in 2071 and happens all over the
solar system. Long distance travel relies on "hyperspace gates." In 2021, there was a major hyperspace accident that pretty destroyed a large portion of the
Moon. As a result,
Earth now has an
asteroid belt and is constantly bombarded by
meteors.
Venus has been
terraformed, and
Mars has large habitable areas.
A few of the ships which appear in Cowboy Bebop:
The Bebop
This is the large ship where much of the series takes place. It's
Jet's ship and was bought second hand on
Ganymede. It was supposedly a fishing ship, which makes the rest of the character's ship names make a little more sense(
Swordfish?
Redtail? They're all named after fish).
The Swordfish II
This is
Spike's ship. It's a small red racing ship with wing-mounted machine guns and a plasma cannon.
The Redtail
This is
Faye's ship. It's a squat blue ship with gun arms that also prop the ship up when it's on the ground. It has two machine guns as well as rocket launchers. She can control is with a remote hidden in her bracelet.
The Hammerhead
This is
Jet's combat ship. It's a small brownish ship with a swivel arm on top that fires a grappling claw.
Space Shuttle Columbia
Ok, it only appears in one episode, but it's still there. Doohan, the mechanic who made the
Swordfish for
Spike, has fixed up the original space shuttle
Columbia. In episode 19(
Wild Horses) he actually pulls it out and flies it.
A few memorable one-episode characters:
Pierrot Le Fou
This character, who appears in the episode with the same name, is a giant killing machine. He wears a suit, an undershirt with a frilly white collar and a
top hat. He carries an insanely large amount of
weaponry and uses a gun built into his cane.
Andy
Andy is another bounty hunter they meet in Episode 22,
Cowboy Funk. Andy takes the on going
cowboy/
bounty hunter theme a step too far. He rides around on a horse, wears a cowboy outfit, uses a
six-shooter and asks people to call him
Wyatt Earp. His personality is very similar to
Spike's, which leads to no end of conflict between the two.
Doohan
Doohan appears in Episode 19,
Wild Horses. He is the mechanic who built the
Swordfish and gave it to Spike. He is of a philosophical bent regarding machines. On his assistant's suggestion that they add something to silence the
Swordfish's engine, he comments "If you put one in, then I can't hear what it's telling me." When his assistant goes further and suggests adding a better computer system and autopilot, he says "Do you want to use a machine or do you want the machine to use you?"
A few characters from Spike's past:
Vicious
This is a character from
Spike's past, and is a member of the Red Dragon syndicate. He always has a large black bird with him and fights with a sword. He is a villian that appears occasionally in the series.
Julia
Another character from
Spike's past,
flash backs of her are certain to appear in any episode involving
Vicious. Who she is, and what relation she is to
Spike and
Vicious would definitely be called a spoiler, so I won't spend any more time on her.
The Jazz Connection
Aside from an excellent soundtrack featuring plenty of original
jazz music, the series and one of the ships being named after
a jazz movement, and most of the episode names refering to jazz songs or styles there's also the occasional
jazz reference in dialogue. For example, at the beginning of episode 3 (
Honkytonk Woman)
Jet claims to have had a dream where
Charlie Parker told him "Only hands can wash hands."
Jet uses this dream to rationalize making a ton of money at a casino.