Along with many alread quoted:
The end of Hermes’s Bureaucracy song:
Bender: “I am Bender, please insert liquor!”
The whole sequence in “Brannigan Begin Again” (I think that’s the right title) that parodies Midnight Cowboy just sends me rolling off the couch every time I see it.
Zoidberg, courting Edna on his home planet:
Fry: “Tell her she looks thin.”
Zoidberg: “You look malnourished. Do you have internal parasites?”
This thread makes me ridiculously happy. 
I like this bit from “The Day The Earth Stood Stupid”:
Leela: Ow! Fire hot!
Professor: The Professie will help! [reaches into fireplace to retrieve burning note] Waugh! Fire indeed hot!
…okay, that one doesn’t really work in text, but it’s inexplicably hilarious in the episode.
BTW, I got the “You changed the outcome by measuring it!” joke, and I’m an English major.
You know, no matter how much an IT guy likes Futurama, when something goes wrong with your computer, I’ve learned it’s a bad idea to toss this quote at him.
Anyway, my boyfriend and I can’t drink or be near that fizzy white beverage without calling it Cham-pag-in in an ultra pseudo-sexy voice.
Why yes! Thank you for noticing.
–Cliffy
Greatest Fry line:
Coin-operated gypsy: Have you heard of the Monks of [something or other]?
Fry: I’ve not heard of them.
It’s all in the delivery, which is so perfect I’m just waiting for the opportunity to use this line myself.
From “Anthology Of Interest I”:
Mr. Pannuci: Hey! You forgot your pizza.
Stephen Hawking: Throw it in the garbage.
and
Hawking (stealing Fry’s idea): I call it a Hawking hole…
Maybe it’s just that computerized voice…
also —
I love the episode when Bender adopts the orphans, and he entertains them by reading his arrest record (and shows them his mug shot).
“A Pharoah to Remember” does have one great moment when the Priests are choosing a new Pharoah:
High Priest: Great Wall of Prophecy, reveal to us God’s will so that we may blindly obey.
Worshipers: Free us from thought and responsibility.
High Priest: We shall read things off you…
Worshipers: …and do them.
High Priest: You’re words guide us.
Worshipers: We’re dumb.
From the episode where Bender turns into a were-car (why no Transformer jokes?):
A classic riff off all the Universal Horror Classic flicks. 
And from the same episode–
Bender: Ahhh, Christmas Eve. Another worthless day where I accomplish absolutely nothing.
I love those monks
Trapped Monk: “Let us out! We cooked our shoes in the dryer and ate them! Now we’re bored!”
and (horribly paraphrased)
Monk 1: “He speaks out of love for his friend. What if this love is God?”
Monk 2: “Oh, how convenient, a theory about God that doesn’t involve looking through a telescope! Get back to work!”
Preacher Bot: Wretched sinner unit the path to robot heaven lies here, in the good book 3.0.
Bender: Hey, do I preach to you when you’re lying stoned in the gutter? Noooo, so beat it.
Fry: Who was that guy?
Bender: Your momma. Now shut up and drag me to work.
After Zoidberg’s underwater shell house burns down.
<Zoid> How did this happen?
<Hermes> confused That’s a very good question…
<Bender> Oooh, that’s where my cigar went.
<Hermes> THAT JUST BRINGS UP MORE QUESTIONS!!!
I just found this quote on a website, from an episode I haven’t seen yet. May be my new favorite:
Gay Hippie: They called me crazy for building this ark.
Old Hippie: You ARE crazy. You filled it with same sex animal couples.
Gay Hippie: Hey, there are parts of the bible I like and parts I don’t like.
And my favorite bit from the Star Trek episode:
Bender: But what about those of us who don’t like “Star Trek?”
Walter Koenig: Yeah!
Fry: I’m gonna spin until I fall down! [completes half a spin and falls down]
For some reason this always cracks me up. Similarly:
Fry: I’ve got an idea.
Leela: [instantly] I’ve got a better idea.
Of course hearing Sigourney Weaver as the ship was a wild combination of sexy and really really really creepy.
Calculon “Great Shatner’s ghost.”
Love the fact that a hammy robot actor should revere the Shat-Man.
Oh, another good one from the episode I quoted above…
<Bender> (After failing to pour wine from a sunken pirate ship into his mouth underwater) Aaarr…the Laws of Science be a harsh mistress.
“I was all of history’s great acting robots! Acting Unit 0.8, Thespo-mat, David Duchovny!”
One of my favorite episodes that hasn’t been mentioned yet is “Teenage Mutant Leela’s Hurdles.”
The sequence that cracks me up the most is the complete insensitivity of Fry, Bender and Zapp when they’re captured in “Amazon Women in the Mood.”
Favorite Episode: Roswell That Ends Well
President Truman to Zoidberg: Are you here to create some kind of human-alien hybrid?
Zoidberg: Are you coming on to me?
President Truman: Hot crackers! I take exception to that!
Zoidberg: I’m not hearing a no.