In the manga, Wolfwood looked like he was dying, and Vash was all like "DOOOOOOON'T DIIIIIIIIIIIIIIIIIIEEEEEEEEEEEEEEEE!" and Wolfwood was stating that he was only going to sleep.
The Big Lipped Alligator Moment with the black guy giving them the coin and asking whether they prefer fish or clams.
Vash's full name in the anime.
The episode with the drunken gunsmith. The end with Vash and the barkeeper.
Vash: AHAHAHAHA! HEY LADY WHATCHA WAITIN FOR, FILL ER UP!
(Barkeeper bonks him over the head with a beer pitcher)
Vash: I mean please fill er up miss, if you wouldn't mind.
Barkeeper: That's better.
Earlier in that same episode:
Vash (who's drunk off his gourd): Gimme...gimme back mah gun grandma...(gets hit in the face with his gun) * THWACK!*
And he still catches his gun!
Another episode, the famous "Genocide Song":
Vash: (singing) Total slaughter... total slaughter... I won't leave a single man alive... la dee da dee daa... genocide... la dee da dee daa... an ocean of blood... let's begin the killing time.
Thug 1: He's... singing?
Thug 2: What horrible lyrics!
Big Bad: Stay right where you are. He's just trying to scare you.
Vash: (sighs) I knew it wouldn't work.
And another episode:
Vash: THE DEADLY DODGEBALL HEAD! A simple technique to hold the ball in place with INTENSE SUCTION! Try this at home, kids!
Which brings in mind the first episode's Establishing Character Moment: the bad guy of the week is armed with a big-ass boomerang. Vash leaps over the weapon and sabotages the retraction mechanism so that it will wrap around the bad guy and squeeze him into submission.
Vash: (makes a cat-face) Dangerous toys are fun but you could get hurt!
"The man who will slaughter the innocent! Does the MOST evil of evil deeds with a price of sixty billion double-dollars on his head! YES I AM THAT MAN!"
When Vash mentions his full name.
Most of the bar scene in Badlands Rumble, especially the part where Vash manages to steal the bullets out of everyone's guns without them noticing, and drunk Meryl.