Or, "In which Neshomeh overuses the word 'awesome' and depletes her quota for the rest of the month."
"Favorite Character" is a bit complicated, so I'm going to have to break it up.
First Favorite Character
The character I first fell in love with is Pilot. That's not his actual name—it's never explicitly stated that he has a name—but since it would probably be a gazillion syllables long if he does have one, he's called Pilot. He is, in fact, Moya's pilot, but he's a lot more than that. Leviathans and Pilots share a symbiotic relationship, so he's also her companion and translator, and he's the one who makes sure all the life-support systems (which Moya does not need to live) keep working in addition to regulating everything else. He's a pretty important dude.
Unfortunately, he's also pretty much the last guy who should have his job. He's young (for his species—creatively also referred to as Pilots), has very little experience, and boy oh boy, the baggage. Everybody on Farscape has baggage, but his is pretty epic. I can't say any more, because that would be spoiling.
Generally speaking, Pilot is mild-mannered (save the occasional snippy remark) and works hard to do well by Moya and the crew, but there's only so much one person can take, and when he gets fed up you'd better watch out. It's not a good idea to piss off the guy who controls the ship. The rare moments when Pilot totally flips his lid are some of the most dramatic due to how bad it has to get for that to happen, and how much worse he can make it when he has a mind to.
So, there's all that personality and character arc stuff—though he doesn't get nearly enough screen time, IMO. What there is is awesome, but... ah, never mind.
Also, he's one of the Henson creatures I mentioned, so he's just amazing to look at. He's about as far from humanoid as you can get. He's got a head with two eyes and a mouth, but the similarities end there. I can't describe him adequately, so have some pictures!
Even those only help so much. Most of them don't really show that he's got four arms. They also don't show that he's huge: his body stretches way down, and ends in tendrils that are biologically bonded to Moya and run pretty far throughout. In real-life context, a puppeteer fits inside his upper body to do large turning movements and such; there are at least five guys who operate him. He's just really, really cool all around.
Second Favorite Character
Not second-place, just... second. The one who's grown on me most over the years, basically: Ka D'Argo, the Luxan warrior. His growth over the course of the show is really, really beautiful. He fills out the obligatory tough guy archetype, and he does it well, he's very macho and all that. He's also a simple guy with simple dreams, and you can't help but sympathize with him as you start to see all the crap goes through for them. D'Argo carries important themes of prejudice and racism on his big, muscly shoulders. These themes abound, considering that the Peacekeepers have a thing about not mixing with other species, but I'd say D'Argo's the one whose arc most highlights them.
He is also hilarious. He is the best at trying and failing to understand John's human idioms, and his own humor is surprising and awesome. It's a bit black, and a bit sarcastic, and a bit self-aware. It's one reason I started paying more attention to him.
Also, Scorpius.
Scorpius. Phobos already talked about Scorpius, but let me just take a moment to heartily second him. Scorpius is freaking awesome in every possible way and he gets my number one spot. (That Malfoy kid is gonna have to work damn hard to even scratch worthiness to share the name.)
... I am noticing that my top three are all dudes, so let me just add that the female characters all kick ass, too. Not one lady on this show is weak in any sense whatsoever. Oddly enough, my least favorite is the healery one—her writing is not quite as strong as the others', I think—but she still kicks ass. You don't want to mess with Zhaan.
Favorite female character is the lead, Aeryn, though. This might have to do with the fact that she has a great relationship with Pilot (that, like him, does not get enough screen time). And Chiana is v. v. fun, as Phobos said.
... I could tell you why almost every single Farscape character is awesome, but I have to wrap this up because it's past my bedtime.
Favorite Episode
Oh god... uh... well, the second season's ninth episode, "Out of Their Minds," has a special place in my heart because it's the first one I ever saw, and it hooked me. It's a body-swapping episode, so I had no idea who these people were or what was going on except I think a friend had told me about the show once months previously, but really no clue. And it was awesome. Farscape boldly goes where other shows fear to tread, so my first exposure to the show and the characters involved working out how to pee (and properly stow the equipment afterward), a man's shameless and juvenile response finding himself in a body with boobs, and why it's a bad idea to swap an extremely complex, multitasking-capable mind into a relatively limited biped brain, and vice versa.
(Also red acid vomit that can creep upward, but that's unrelated.)
"Crackers Don't Matter" is a fantastic cracked-out episode. Another great cracked-out ep is "Revenging Angel," though (season 3, ep 16). It's the result of the show's producers sitting around and discussing why doing an animated episode would never work, and then deciding to go ahead and do it anyway. And frell me if it doesn't work.
Season 1's "DNA Mad Scientist" is pretty high up, too. It's one of the darker, more serious ones, wherein some pretty horrific stuff goes on. It's about Pilot and Aeryn and how the crew can be utter bastards to each other when a chance to serve themselves comes along. This decreases as they spend more time stuck together and dependent on each other, but in the first season they're almost as dangerous to themselves as the actual bad guys.
I totally failed at wrapping this up. Oh well.
~Neshomeh, gonna go pass out now.