You can actually hear the "Why me?" in Marlin's tone during this scene:
Dory: See, I suffer from short-term memory loss. Marlin: Short. Term. Memory loss... I don't believe this. Dory: Yeah, I forget things almost instantly. It runs in my family... at least, I think it does... hm, where are they? [pause] Can I help you?
"I shall call him Squishy and he shall be mine and he shall be my Squishy. Come here, Squishy!"
The scene when Marlin and Dory enter the dark part of the ocean:
Marlin: Dory, do you see anything? Dory: Ahhhh! Something's got me! Marlin: That was me; I'm sorry. Dory: (gasp) Who's that?! Marlin: "Who's that?" Who could it be? It's me! Dory: Are...are you my conscience? Marlin: Yeah, yeah, I'm your conscience. We haven't spoken for a while. How are you? Dory: Mmm, can't complain. Marlin: Eh, good. Now, Dory, I want you to tell me...do you see anything? Dory: I see a...I see a light. Marlin: A light? Dory: Yeah, over there. Hey conscience, am I dead?
"Hey, look. "Es-ca-pay". I wonder what that means? That's funny, it's spelled just like the word "escape."
"No eating here tonight; you on a DIIIIIET!"
Dory talking in her sleep.
"Careful with that hammer... sea monkey has my money...Yes, I'm a natural blue..."
The DVD reveals alternate ad-libs by Ellen: "Mmmmm.... no whammies.... Stop!"
Dory singing completely happily "Just keep swimming...just keep swimming" when she's stuck in the net with the other fish who are swimming down and repeatedly saying "KEEP SWIMMING!"
Marlin goes from crowing, "The clownfish is the winner!" to Oh, Crap when he realizes Dory didn't make it out of the jellyfish forest. He swims as fast as he can back into it to find her, and finds her in the tentacled embrace of one. Grabbing her away, Marlin tries to find a way out— and Dory, barely conscious, murmurs about their game, "Am I disqualified?"
Marlin refuses to let Dory ask a whale for directions to Sydney out of fear that it will eat them. It does, but they get better.
Marlin: Okay, now it's my turn. I'm thinking of something dark and mysterious. It's a fish we don't know! And if we ask it directions, it could ingest us and spit out our bones!
Marlin: I don't want to play the gender card right now. You wanna play a card? Let's play the "not die" card.
While they're trying to escape from Bruce, Bruce is slamming against a door they went through and Dory calls out, "Who is it? ... Sorry, you're gonna have to come back later! We're trying to escape!"
"I'M GONNA TOUCH THE BUTT!"
Marlin: Nemo! Don't Touch the Boat!
Nemo: *Touches the Boat*
On the DVD Commentary, Andrew Stanton (Director) is being mocked for all the voices he did for the movie (Crush, the seagulls, and others). He comments that there was no way that part was going to make it onto the disc (which it did).
Considering that the "ring of fire" is simply the bubbles from a fish tank underwater volcano, the sheer deadly seriousness with which everyone approaches Nemo's initiation ceremony makes the scene both surprisingly tense and utterly hilarious:
Peach: Surely there's another way! He's just a little boy!
Turtles are funny.
Deb introducing Nemo to her twin sister Flo (actually her reflection in the glass tank).
The very very very end of the closing credits, when the little green fish from the Sharks' meeting EATS the angler fish!
During Darla's visit to the dentist when everything's going nuts, and the reaction of the people in the waiting room.
Mr. Ray, the overly-cheerful kindergarten teacher who is just a tad too into the material, singing constantly, even to the parents. During the fight between Marlin and Nemo, the mood is ruined for the audience when Mr. Ray tries to get the other children not to look!
"THEEEEEEEEEEEEEEEEEEEEEEEEERE'S nothin' to see here! Gather! Uh... over there!"
None of the children in his classroom ever take him up on his offer to, "Come on, sing with me!" (Although they are kindergarteners; the scientific names are probably a little much for most of them.)
"OH MY GOSTH! NEMO'TH THWIMMING OUT TA' STHEEE!!!"
"False alarm." (In the fullscreen version, we actually see the female patient's legs.)
Mr. Ray blanketing all the little fish kids with his body and saying, "Oh! I wonder where my class has gone?"
Marlin and Dory are being guided by Bruce through a foreboding part of the ocean filled with mines. He takes them into the submarine, where two of his friends are delighted to see him— "We've already gone through the snacks, and we're still starving!" Marlin gasps and closes his eyes, figuring those sharks will be the the last thing he ever sees— and then ring the bell, we're in the middle of an AA meeting!
For that matter, their first appearance when Nigel is trying to eat a crab:
"OH, WOULD YOU JUST SHUT UP?! You're rats with wings!"
Not only is their portrayal dead-on, but it's also funny as hell. Doubly so for the end of the chase sequence where the stupid birds get stuck in the sail. "Minemineminemineminemineminemineminemine!" indeed.
Special CMOF points to Disney for putting animatronic seagulls outside the Living Seas exhibit at Epcot when they integrated Finding Nemo into it.
The moonfish, especially when they imitate Marlin.
The "Exit Buddy" scene which has Squirt trying to explain safety procedures to Marlin and Dory.
Squirt: Good afternoon, we're gonna have a great jump today! (Cut to Marlin and Dory's blank faces) Okay! First crank a hard cutback as you hit the wall! There's a screaming bottom curve, so watch out! Remember: rip it, roll it, and punch it!
Marlin: I think he's trying to speak to me, I know it! Look, you're really cute, but I don't know what you're saying!
Crush tells them to find their exit buddy. Dory promptly reaches to the side and grabs Marlin hard enough to make his eyes pop out a bit, without either of them saying a word or looking away from Crush.