Leela: Hey! You know what would be a hoot?
Professor: No!! Why would I know that?!
One I like to use as a snappy comeback when it fits.
I never miss an opporunity to say, “Cheese it!”
“Now Zoidberg is the popular one!” - My new SO said this after sex the other day. I’m one lucky girl, right? 
Except for that one where he said “News, everyone!”
Dwight: I heard that alcohol makes you stupid.
Fry: No I’m… doesn’t.
“Morbo congratulates our gargantuan cyborg president. May death come quickly to his enemies.”
“So…humans have easily injured knees. My race will find this information very useful indeed! MUUUAA HA HA HA HA HA HA!!”
“Puny Earthlings were shocked today to learn that a ball of garbage will destroy their pathetic city of New New York.”
"Makes me glad we live here in Los Angeles.”
“Morbo agrees. MUUUAA HA HA HA HA HA!”
Bender (As Flexo) : “But going through divorce together. You can’t tell me that didn’t bring us closer.”
Same episode Bender said “I hate the people who love me, and they hate me!”
Fry: “If it’s that dangerous, why don’t we just send in the robots?” Bender: “WHY, YOU SON OF A…” (as Bender nearly throttles Fry… I guess that’s why)
Fry (to Robot Satan): “Wouldn’t a fiddle made of gold sound really crappy?”
When Hermes is going to jump off the Planet Express building.
Bender: Do a flip.
Hooker bots-We love you Bender!
Bender-Shut up baby I know it!
So many good ones…
“I so desperately want to believe that… so I do!”
“That was so bad I think you gave me CANCER!”
“That equals true!”
“P.S. Cashier’s check!”
“We will start with the firemen, then the math teachers, and so on in that fashion…”
“We will raise your planet’s temperature by one million degrees a day - for five days - unless you give us McNeil!”
Brannigan: “You win again, gravity…”
Professor: “Choke on that, causality!”
Bubblegum Tate: You dare laugh at the jesters of dunk? We came here to terrify and humilliate you, not tickle your funny bones. Watch, as I humilliate your civilization by passing the ball to Curly Joe… only to have it stay in my hand with elastic!
Bugglegum Tate: Sweet Clide, laugh derisively at them!
“She’s built like a steakhouse, but she handles like a bistro”
BENDER [getting kicked out of a theme park]: Forget your stupid theme park! I’m gonna make my own! With hookers! And blackjack! In fact, forget the theme park!
Cherry picked from IMDB:
Dr. Zoidberg: And that’s the story of how I got my new shell. It looks just like the one I threw out yesterday, and I found it in the same dumpster. But this one had a live raccoon inside.
Rich Little: [imitating Howard Cosell] The Vegas odds tonight stand at an unprecedented 1000 to 0. A bet of zero dollars on Bender pays 1000 dollars if he wins. Still, very few takers.
Fry: I’m not a robot like you, I don’t like having discs crammed into me… unless they’re Oreos… and then only in the mouth.
Bender: Hey. What kind of party is this? There’s no booze and only one hooker.
Cubert: “A cigar?”
Tinny Tim: “Ripping!”
Dwight: lights it “Look! I’m Bender!” pukes
Hermes: “Ras H. Tafari! What’s going on here?”
Farnsworth: “The ruffian smoked one of your cigars!”
Hermes: “That’s not a cigar! Uh, and it’s not mine.”
The laughter after this quote cracks me up.
“Please Mr. Nixon, we’re appealing to your sense of decency.”
Even Nixon thinks it’s funny.
Nibblonian: You are the last hope of the Universe.
Fry: So I really am important? How I feel when I’m drunk is correct?
Nibblonian: Yes, except the Dave Matthews Band doesn’t rock.
In that same episode:
Fry: [Is it] because I’m so smart?
The Nibblonians’ laughter, including one’s very George Takei-ish “Oh, my” always cracks me up.