“Now Zoidberg is the Popular One! Hooray!” is the line that keeps being repeated on, and on, and on in this household.
Hooray!
… that said (or posted)… there should also be a Zapp Brannigan Appreciation Society.
I’m just sayin’.
My favorite Zoidberg line happens to come from my favorite episode:
“Once again, the conservative, sandwich-heavy portfolio pays off for the hungry investor!”
Zoidberg on a rampage at the gym (in the episode when he’s trying to mate)–he runs into the water exercise class for pregnant women bug-eyed and screaming:
ZOIDBERG: BUGABUGABUGA
<a woman screams, and we hear the sound of a splash and a baby crying>
INSTRUCTOR: Is there a doctor in here?
ZOIDBERG: I AM a doctor!
<all the women scream and we hear sounds of MANY splashes and babies crying>
Hooray!
Hehe, rowbuts…
The best thing about Zoidberg is that he sounds like (of all people) George Jessel.
A friend of mine has figured out that the best way to do a perfect Zoidberg impression is to talk with a plastic spoon in your mouth.
Try it, you’ll see. 
One of my favorite Zoidberg related lines is, in the first episode you see him.
The Professor tells Fry that he needs a physical and so will have to be examined by the doctor, and then he says, “I have to warn you, though. He’s a little unusual.” Then he lowers his voice and tells Fry, “He wears sandals.”
“On my planet, clam eats you!”
(after breaking a bottle)“Oh no! The professor will hit me! But if Zoiberg FIXES the bottle… perhaps gifts!”
I love Zoidberg. As far as supporting characters go, he’s up there with Zapp Brannigan (and Elenfair is right, we need a Zapp apprectiation thread, too).
But my favorite “side character” is Morbo.
“Mwah ha ha ha ha! Oily humanoid.”
“Kittens give Morbo gas.”
Not necessary for some of us. I consider my Zoidberg impersonation to be one of my better ones. 
Might try the spoon thing sometime anyway…
Kiff, I have mated with a woman. Inform the crew.
“Look at me! I’m Dr. Zoidberg . . . Homeowner!”
He’s just so darn proud.
Well, then, feel free to disregard–it’s only for the Zoidberg-impaired.
P.S. Hi!!
“Refresh my memory. Disemboweling your species: lethal or non-lethal?”
“Lethal.”
“I’d like to place a large wager on myself.”
the episode “Parasites Lost” is a quotable Zoidy goldmine…
<Hermes> He’ll be as strong and flexible as Gumby and Hercules combined…
<Zoidy> Gumburcules? i love that guy!
<Prof. F> these netsuits will allow you to experience Fry’s worm infested bowels as if you were actually wrigging thru them
<Z> There’s no part of that statement i didn’t like
Shotgun, awww…
<Z> Quick, we can escape thru that nasal capilary into the sinus
<H> strange, usually you don’t know anything about Human anatomy
<Z> I learned it from a decongestant commercial, “Soothing Action, action, action, action”
It’s good cholesterol but it spreads like bad cholesterol
<Prof. F> We’re in the heart, better known as the love muscle
<Z> where the food is digested
<Prof. F.> the Pelvic Splanknic Ganglia
<Z> I’ve heard of that, who said i haven’t
Ahhh, Zoidberg! My favorite Zoid quote is very simple: “Gracias”.
It’s the delivery that makes it great!
Also, “Friends, help! A guinea pig tricked me!”
Hi, how’re you? We’re all fine here…
“Greetings everyone [sub]act naturally[/sub].”
“It just so happens I have mail order degrees in muderology AND murderonomy! Zoidberg is afoot!”
“What a man! I’d follow him to Hell and back, I would!”
“One art, please.”
We should have a Zoidberg vs. Zap thread.
–Cliffy