Mad props to the most famous anime series out there. It definitely deserves this, and then some. This is probably because it was seriously made with the American audience in mind, as you can tell by the constant use of English text and themes. But it has its own merits too, like awesome characters, plots, and premise.
The name of the show tells you nothing, until you're introduced to the show. You see, the two original main characters, Spike Spiegel and Jet Black, are bounty hunters. Spike calls himself a "cowboy" since saying "bounty hunter" ain't exactly the best way to make friends. So "Cowboy". And "Bebop" because the show has awesome music, and the ship's name is inexplicably Bebop. Why exactly they chose to name their ship that, I don't know.
The plot of the show deals with Spike and Jet flying around the Sol system trying to pick up bounties and, to their credit, occasionally succeeding. As the series goes on they pick up new passengers.
Let's see a quick character list, in order of appearance:
Spike Spiegel - The main character of the show, in all fairness. He's an ex-gangster who left the world of organized crime for the slightly more respectable world of bounty hunting. He's a good fighter, both with a gun and unarmed. He's also very easy-going and doesn't do much work, except for when he's trying to get a bounty. Still, he's cool under fire and is definitely 'ard.
Jet Black - My personal favorite character, this guy is also quite 'ard. He's an ex-cop who owns the Bebop and keeps it running. He has a bionic arm, even though in the future it's just as easy to get the arm regrown. Jet does a lot more work than Spike, and is a lot more level-headed. He's still cool though, and because he's so level-headed he's sometimes a lot more relaxed than Spike is. Even though he's not as young as he used to be, he can still defend himself in a fight.
Ein - Ein is a Welsh Corgy, a very cute little doggy. He's really smart because he was born and raised in a lab to be a "data dog", which apparently makes him really valuable, and leads him to the Bebop after some misadventures. Mostly though he just walks around the Bebop and looks cute.
Faye Valentine - Hey, you gotta attract guys to the show, and what better way then by giving the show a babe. That's exactly Faye's role, but like everyone else on the show she gets to have a dark past. She's apparently a famous gambler who never lost, but got in an accident and woke up decades later in a hospital with no memories. She sometimes helps Spike and Jet out in trying to round up bounties, but she takes more pleasure in giving them a hard time when they fail. Even though she's the show's babe, she still somehow manages to avoid be completely one-dimensional, which is a relief. She joins the Bebop when she needs a way off a planet where she's gotten mixed up with the criminal element.
Ed - "Radical Edward" was apparently the best hacker on Earth. Exactly who he is though was a matter of some confusion among Earth's inhabitants, leading to one of the funniest lines in Cowboy Bebop so far. Ed, it turns out, is actually a girl, a young child who is almost feral in her actions, but still excitable and fun-loving like any other kid. She gets aboard the Bebop when it comes to Earth looking for a bounty on whoever was drawing graffiti on Earth from a satellite. When it turns out to be the satellite itself doing the graffiti, the Bebop starts to leave but gets turned around by Ed's hacking and is forced to pick her up and let her join in the adventures. Despite being a super-genious and a planet's best hacker, Ed seems to mostly run around the Bebop animal-like and poke her nose into what the others are doing.
Since I'm being thorough, here's a short list of the ships on the show:
Bebop: Jet Black's ship, this is the characters' means of getting around the system and their home. It's large, bulky, and apparently unarmed. Still, it fulfills its purpose well. It also carries the other ships.
Swordfish - Spike's ship. This fighter is named "swordfish" because it has a large gun in front that can do a ton of damage, but takes forever to charge, which means that Spike spends more time using the machine guns on board. I love the way the controls on the ships look, but you'd have to see it to know what I'm talking about.
Redtail - Faye's ship, this thing is filled up with all sorts of weapons and countermeasures. In addition to its machine guns it has missiles and all sorts of useful evasive things to get out of bad situations.
Hammerhead - Jet Black's other ship, used mostly when the other two aren't available. It's named Hammerhead because, well, it looks like one. It seems to be unarmed except for a grappling hook-type thing, which is probably why it gets used so little.
I gotta really quickly rave about a certain episode, episode 11. It's a "filler" episode in that the plot isn't advanced and there are no bounties involved. Instead, it serves as a tribute to some famous sci-fi movies. "Alien" is most obviously represented, since the whole premise of the episode is almost exactly that of "Alien": a creature is on the ship, taking out people one by one and hiding in the ship's vents. Also, Spike makes himself a motion tracker exactly like in "Aliens". He also has the "Predator" tribute, which is an infrared viewer that looks just like the Predator's vision. I'm sure that better sci-fi buffs than me could find even more tributes in this episode. Please tell me if you see something!
Cowboy Bebop is definitely one of the best animes out there. It has none of the cartoonishness that ruins other animes, even though Ed is rather silly (but it doesn't hurt the show). In fact, this is the one anime in which I've actually laughed out loud at the jokes. But apart from the silly side, this show has an awesome serious side. Like I said, the three main characters all have mysterious pasts which you slowly learn about as the show progresses. The fight scenes are awesome, and the bounty chases are always cool. The main plots, like Spike's conflict with the gang he used to be a part of, is well done and exciting.
And the music rocks! Almost every episode features a different music style, and it always helps the episode a ton! It sets the mood and really helps you feel the emotions of the events. No wonder there are like five different Cowboy Bebop soundtracks out there!