Absolute Anime

There are so many I don't know where to start but here are the ones that I remember the most.

Gundam Seed
When Athrun tells Cagalli she has a crab down her shirt Cagalli accidentally showed Athrun her boob and he fell down and accidentally fired his gun. Priceless.

The look on Athruns face when Lacus came back after be held hostage. He looked down at her stomach and said "huh?" It looked like she was pregnant because her dress was inside the suit.

Trigun
loads of funny crap happend but when Vash was running from a whole town trying to get the 60 billion bounty on his head I was rolling on the floor when I first saw it.

Chrono Crusade
When Rosette and Chrono were in Los Vagas and Resette was shacking her butt in Chrono's face trying to get some more money out of him I'll never forget the look on his face.

In Assemble Insert: when Maron first meets with the Demon Seed evil mecha she needs to stop. She stands there posed dramatically...and then turns to her boss and tells him "I forgot my lines!"

In Excel Saga: for me the funniest scene is when Watanabe asks Hyatt what her name is...and out pops Nabeshin boldly proclaiming "It's Nabeshin!"

In You're Under Arrest: after Santaman states his bike's name, he's asked to repeat it...and it's so long that he can't remember it.

In Colorful: when Steve tries to get an upside-down Mt. Fuji shot...and falls into the reflecting pool.

That's all that come to mind right now.

Full Metal Panic! when Sosuke is training Tessa for the battle against Mao. Tessa is climing up the ladder when she falls and lands on sosuke, they have a breef moment before the sun goes down.

Pretty much all of Excel Saga and FLCL.

Full Metal Panic
When Sosuke was following Kaname around he kept on telling her it was a Co-incidents.

Full Metal Panic!
When Koname shows up at Sousuke's house when Tessa is in the shower.

kurz wrote:Full Metal Panic!
When Koname shows up at Sousuke's house when Tessa is in the shower.

Episode 9 of Trigun presents a couple very funny moments. First, when Vash is introducing himself to Wolfwood:

Vash: My name is Valentinez Alkalinella Xifax Sicidabohertz Gombigobilla Blue Stradivari Talentrent Pierre Andri Charton-Haymoss Ivanovici Baldeus George Doitzel Kaiser the Third. Don't hesitate to call.
Milly: Ha ha! What are you talking about, Mr. Vash the Stampede?
Vash: I HATE IT WHEN YOU CALL ME BY MY FULL NAME!

And then later on, when Vash and Wolfwood jump off the bus to rescue the girl:

Vash: What are you doing?
Woldwood: Don't ask questions. I'm going to save the child.
Vash: With your bare hands?
(Wolfwood realizes this, fumbles around his shirt for a moment, then turns back and looks at the disappearing bus).
Wolfwood: OH S*beep*!

Here's another funny moment, and it's unique to dubs. It's from episode 1 of Burn Up Excess. It's not so much the words themselves but rather their context. I'd give the quote verbatim, but it's extremely naughty. Just go to her profile--it has the scene in it.

Blue Gender

"...... you might actually have to use that gun on your hip .... or did you just think it was a fashion accessory that came with the uniform?"

Don't remember who said it. I just know I loved the line.

Full Metal Panic? Fumoffu!!!

When Sosuke and Kaname run back to school to take their test Kaname trows Sosuke in front of a cab to get it to stop.

Sosuke: you almost killed me.

Kaname: SHUT UP AND GET IN!!!!!

Then later on Kaname tried to trow Sosuke off the train because they got on the wrong one she was screaming die Sosuke die . Then at the end it turned out that the class was canceled cause the teacher got sick.

That bit from Chrono Crusade was great. In my mind (first episode), there's also:

Elder: "Hehehehe! I see Paris, I see France, I see someone's underpants! Hahahahaha!!!"
Rosette: "Eeeeeeeeeee!!" (Wails)
Elder: "And today's pair was almost as wild as the French ones!" (or something like that)
Rosette: "Dirty old man! I'll kill you with this spoon!"
Not how the original Japanese version goes, but oh well. Elder's comment's a killer. Go John Swasey!

Oh, and personally, Misaki and Icchan's second meeting (Angelic Layer)

Nothing like a creepy guy in a labcoat jumping down from a tree, only for his legs to fall asleep, then for him to spring up with a "I'm wiggly Icchan!" before falling back down again.
Oh, and of course...

"Your punishment... ten minutes with a live octopus in your pants!"