The following is probably not word-for-word accurate as I have yet to find a Futurama script resource, but . . .
LEELA: Fry, since you came to the future, you’ve become a fat sack of crap.
FRY (indignantly): Sack?
…
BENDER: Look! I’m steering with my butt!
FRY (with great enthusiasm): Now that’s the best thing I ever saw!
Bender (singing and playing banjo):
“We got a right to pick a little fight with rustlers,
Somebody wants to pick a fight with us,
He better bite my ass!
YeeHaw!”
And that in turn reminds me of…
Bender: “Leela, save me! . . . And yourself I guess . . . and my banjo . . . and Fry.”
Favorite Episode: If I had to pick just one, I’d say “Luck of the Fryrish.” But close runners-up would be “Farnsworth Parabox”, “Leela’s Homeworld”, “Put Your HEad on My Shoulder” and “The Day the Earth Stood Stupid.”
Least favorite Episode, hands-down, is “A Pharaoh to Remember.” Basically just Bender being a jerk for half-an-hour. Yes, he’s usually a jerk for whole episodes at a time, but there’s generally other stuff for us to laugh at.
Most of my favorite quotes are already mentioned, but I’ll submit:
Fry, from “A Flight To Remember”: “Don’t worry, Leela, my fake relationship with you is much more meaningful to me than my fake relationship with Amy.”
I love Professor Farnsworth’s utter disregard for the safety of the crew:
“Good news, everyone. Tomorrow you’ll be making a delivery to Ebola 9, the
virus planet.” -Professor
“Why can’t we go today?”
“Because tonight’s a special night, and I want all of you to be alive.”
Another quote that’s all in the delivery. The way he says “virus planet” slays me.
Scruffy: “I ain’t seen him so down… or ever before.”
85 posts and I still have a couple more. These will be paraphrases I am not word perfect on Futurama.
At Elzar’s restaurant
Hermes: There’s jerk ham, jerk chicken, jerk pork, jerk beef. Is there any kind of meat this man can’t jerk?
===
Fry and Bender are at a robot strip joint.
Bender: Man, she is built!
Fry: Yeah, look at that exhaust pipe.
Bender: You’re sick
Bender’s last line was censored out when shown on Channel 4.
===
About a million sight gags. I can’t remember the circumstance for this one (I know someone will)
Someone: But where can we find a doomsday device?
Prof Farnsworth instantly reveals his unreasonably large selection of doomsday devices.
His actual line is “Pervert.” So it makes perfect sense that they deleted it. 
Bender: “Interesting! No, wait. The other thing. Tedious.”
“I guess I can spare one and still be feared.”
“Why Must I be a Crustacean in Love?” has a couple of brilliant sight gags.
My favorite is “Look, my old scuttling ground!”. And the camera pulls back to reveal a car that has six legs and moves like a crab.
And, of course, in the gym, a panning shot moves past a woman pumping several hundred pounds on the kegelcizer.
Dr. Zoid: Hooray! Now ZOIDBERG is the popular one!
Isn’t there a political party that proposes ending the three-day waiting period for doomsday devices? That was funny.
Anything the robot devil says is pure gold (in shape of a violin).
“Hello Bender! We’ve prepared several agonizing and ironic punishments for you!”
“You can’t just have the characters say how they feel! That makes me feel angry!!!”
“These hands keep… touching me.”
Why Frye moves in with Bender. . .
F: Where’s the bathroom?
B: The what room?
F: The bath room.
B: The bath what?
F: The bath room.
B: The what what.
From the one where they become superheroes…
The villan appears on the monitor when Leela, Fry, Bender, and Prof are all in there. Farnsworth is upset, and leela says…
“Isn’t it time for your nap?”
Farnsworth, “YES, DAMNIT!!”
he falls asleep instantly and ignores the superheroe threat and his chair reclines and takes him away.
The best one is when there is shouting between Hermes, and Farnsworth between them and their children. Zoidberg comes in and says, “Is this angry shouting, or busted hearing aid shouting?”
Hermes: “I’m afraid its both”
Farnsworth, “WHAT!?!?!?!”
Farnsworth has the best delievery of any character in the series.
This one really doesn’t work in print, but wot the heck:
At the Clawplaq (sp??) match:
“And now let us rise for our national anthem”
Danger theme from Star trek Commences
Fry: “Oh Crap.”
Farnsworth: Ooooh that makes me so mad! If anyone needs me, I’ll be in the Angry Dome!!!
(when the ship flies out, you see the prof pacing around in a domed area grumbling angrily)
Pet Store Guy: How about this electric snail?
Fry: That’s a stupid animal. You’re stupid! I said I want the best animal!
Bender: Uh oh, is she behind me?
Accountant: No, I’m in front of you.
Bender: Eeee!
(everyone gets captured except Zoidberg)
Zoidberg: What, do I smell or something? sniff sniff …Ohhh.
(at the witch’s lair)
Leela: Why have you brought us here?!
Zoidberg: And why did I have to take a cab?!
One of my favorite quotes, and I chuckle every time I think of it.
Also, as previously mentioned :
Prof. : “While you were gone, the Globetrotters held a press conference to announce that I was a jive sucka.”
“Soon all the planets will be crackin’ wise about our mommas.”
“I’m just glad my fat ugly momma isn’t alive to see this day.”
“We can talk about your promiscuous mother later, Hermes, we’ve got work to do!”
My favorite show of all time. I just finsihed watching the last DVD set recently.
From Spanish Fry
Lrr: Hmm. This jerk chicken is good. I’ think I’ll have Fry’s lower horn jerked.
Bender (off-screen): It’s used to it! Woo-hoo!
My favorite part is when they buy the lap dance for Fry from the huge ovoid robot with the stole. She tips over on him and then vibrates wildly, crushing poor Fry underneath.
–Cliffy
(Later in the episode)
Prof: Did you all take your pressure pills?
Amy (exasperated): Yes! Now stop asking!
–Cliffy
Yeah, that one’s pretty weak, but it did have one classic line:
Fry: You know the worst part about being a slave? You have to work all day, and they won’t pay you or let you go.
Leela: That’s the only thing about being a slave!
Fry: Oh, and you know what else is bad? The hours.