Actually, it was an unnamed woman in the foreground while Amy and the others walked across the back.
Same episode: “New! Windowless room for ugly exercisers!”
Fry: Zoidberg’s got male jelly coming out the wazoo!
Edna: Well, that is where it comes out…
When they’re all super-heroes and visiting the mayor and he tries to summon them, they have to leave so they can come back in in costume.
Bender (as he’s running out the door): Uh, I think I left my apartment on fire!
I use that one sometimes.
Oh, and in the episode when time starts skipping.
Newsreader: Next we’ll be talking about new pop sensation Wendy who last night <skip> won three Emmies before going on to be <skip> found dead in her bathtub.
A nice summary of a lot of pop careers, I think.
There’s a line my youngest brother loves - so we all say it whenever we can - that I just have to post. It’s from Where the Buggalo Roam.
“I am the Man with No Name. Zapp Brannigan, at your service.”
Fry cracked corn, and I don’t care,
Leela cracked corn, I still don’t care,
Bender cracked corn, and he is great,
Take that you stupid corn!
Fry: You could just bend the hatch off this steam pipe…no good, it’s full of steam!!
Who’s the Redhead???
I have all the DVDs, have seen all the episodes multiple times, so I know I’ll feel silly when this is pointed out to me! But I can’t figure out who the redhead is!
At Fry’s funeral, in the scene descibed by Max Torque, one of the Amazonians who had been responsible for carrying out Fry’s (overturned) death sentence in Amazon Women In the Mood laments “Him make good Snoo-snoo.” Camera then pans to reveal all of Fry’s ex-lovers sitting together, they respond with little enthusiasm. We see:[ul]
[li]Michelle, Fry’s on-again/off-again girlfriend of the last thousand years[/li][li]Petunia, Fry’s Valentine date, rounded up at the Bus Station by Bender’s computer dating service[/li][li]Morgan Proctor, Bureaucrat Level 19 “Dirty, dirty boy!”[/li][li]That Radiator Woman From That Radiator Planet, a radiator[/li][li]and a Redhead, who I can’t place[/li][/ul]
Who’s the Redhead???
So many to choose from, but this moment is worthy. The song sequence in “How Hermes requisitioned his groove back”, especially the verse with the other members of the gang taking turns:
Zoidberg: They said I probably shouldn’t be a surgeon.
Farnsworth: They poo-pooed my electric Frankfurter.
Leela: They said I probably shouldn’t fly with just one eye.
Bender: I am Bender. Please insert girder.
According to wikipedia the fifth girl was in “Love’s labours lost in space” and didn’t have a name. Maybe this isn’t your redhead, but I think that’s a lead worth checking out.
You’re welcome. 
“We commend the body of Hermenthotip to the abode of the damned. The damned good looking! Pharaoh commanded me to tell that joke at his funeral.”
The look on his face after delivering the joke is fantastic.
My favorite Morbo line:
“WINDMILLS DO NOT WORK THAT WAY!! GOOD NIGHT!!”
Favorite Lrrr line:
“BLECH! These candies are chalky and unpleasant!”
“And what is this emotion you humans call ‘wuv’?”
“Surely it says ‘love’?”
“No, ‘wuv’ - with an Earth ‘W’. Behold!”
“This concept of ‘wuv’ confuses and infuriates us!!”
“Once again, the conservative, sandwich-heavy portfolio pays off for the hungry investor”
“Guards! Bring me the forms I need to fill out to have her taken away!”
Thank you!
Ah yes, they met at a singles bar “You’re from the 20th Century? I’m from the 21st Century”. They do leave the bar together, Fry takes Bender aside, hands him some money, and says “I’m going to need the apartment tonight. Go see a Saucy Puppet Show.”
This is from memory, but I got the joke part of it:
Bender: I can help you, but you may have to make a metaphorical “deal with the Devil”. By “Devil” I mean Robot Devil and by “metaphorical” I mean get your coat.
(From the episode Fry gets the Robot Devil’s hands.)
Morbo: Morbo can’t understand his teleprompter. He forgot how you say that letter that looks like a man with a hat.
Linda: It’s a ‘t’. It goes “tuh”.
Morbo: Hello, little man. I will destroy you!!
Fry: Man, even the news monster is acting strange.
I love that Fry is so at ease with the concept of a newsmonster.
Although I would love to see the real news read by Morbo. I think there’s a definite market niche there.
Hermes’ song is a good choice. I love the philosophy of the chorus: “When push comes to shove, you gotta do what you love/Even if it’s not a good idea.”
My favorite isn’t a line. From the pilot, when the cops are about to kick down the door, and Bender drops a brick. Sorta. Great sight gag.
From the episode where Zoidberg’s people take over Earth.
Zoidberg: You killed my lawyer!
Ambassador: You’re welcome!
From the same episode, when the Earth slaves are building the oppression ship, and Zoidberg instructs them to keep globbing. Just the way he yells, “GLOB!” in that high, shrieking voice, with spittle flying. Hilarious.
And finally, the beginning and end of Zoidberg’s speech in the first Valentine’s Day episode.
“And then something wonderful happened, and why not?”
“And it would have been even more special if it had also been Valentine’s Day…what? It was? …Hooray!”
From “Godfellows” when Bender encounters the galaxy that signals him in Binary, and turns out to be God…
Bender: What are you? Some kind of galactic computer?
Galaxy: Possible. I am user friendly, my good chum.
Bender: Who built you?
Galaxy: I have always been.
Bender: Oh, my God. Are you God?
"God": Possible. I do feel compassion for all living things… my good chum.
The whole exchange makes me giggle, but the slight delay before “God” says that last “My good chum” is just too much.
From the same scene, I fell out of my chair laughing at the “SEND MORE TRAINS!” bit.
No.
Not a specific moment as such but (as a civil servant working in a central government department) I find the episode “How Hermes requisitioned his groove back” both hilarious and frighteningly accurate.