It’s mentioned again in Two Cathedrals when Bartlet is railing against God and lists all the things God has done to test him. Then he launches into Latin and tells God to shove it.
Many of my favorites already mentioned, so makes it easier to pick - the opening for Galileo V. Where CJ wasn’t saying it right - but Sam did.
The Leo/Jordan scenes from Bartlet for America where Leo talks about his alcoholism…
JORDAN
You had a drink.
LEO
I’m an alcoholic. I don’t have one drink. I don’t understand people who have one drink. I don’t understand people who leave half a glass of wine on the table. I don’t understand people who say they’ve had enough. How can you have enough of feeling like this? How can you not want to feel like this longer? My brain works differently.
JORDAN
Who was the third person in the room?
LEO
Well, now we’ve arrived at our problem.
LEO
I like the little things. The way a glass feels in your hand - a good glass, thick, with a heavy base. I love the sound an ice cube makes when you drop it from just the right height. The sound of an ice cube being dropped into a glass. Too high and it’ll chip when you drop it. Chip the ice and it’ll melt too fast in the scotch.
JORDAN [VO]
I don’t understand how you could have a drink. I don’t understand how, after everything you worked for, how on that day of all days you could be so stupid.
LEO
That’s because you think it has something to do with smart and stupid. Do you have any idea how many alcoholics are in Mensa? You think it’s a lack of willpower? That’s like thinking somebody with anorexia nervosa has an overdeveloped sense of vanity. My father was an alcoholic. His father was an alcoholic. So, in my case…
“In the future, if you’re wondering, ‘Crime, boy, I don’t know’ is when I decided to kick your ass.”
Dammit, I was just going to post that link. 
This thread got me started watching a bunch of West Wing Youtube clips.
“Mike, are you sure you want your one question to be that stupid?” (Link)
For Charlie, who doesn’t have a Dad, from Jed, who didn’t have a son.
I loved the scene when Leo asked Fitzwallace if he would have any problem with hiring Charlie as the President’s “body man”, a young black man carrying his bag and opening doors for him:
Fitz: “I’m an old black man and I wait on the president.”
Leo: “The kid’s gotta carry his bag and . . .”
Fitz: “You gonna pay him a decent wage, treat him with respect in the workplace?”
Leo: “Yeah.”
Fitz: “Then what the hell do I care? I’ve got honest-to-God battles to win, Leo. I don’t have that much time for the cosmetic ones, you know what I’m saying?”
Yay! Thanks 
Well this might make your hair stand on end - it’s cheesy as hell and what on earth was he babbling on about: from … November 1999:
I’ve got so many favourite moments. A lot of them have been mentioned here (pretty much all of In Excelsis Deo; Bartlet’s ranting at God in the cathedral; Abby slicing off the president’s tie and “Unfunded mandate” - though I think the follow-up “Can we have it back?” is better; Galileo V and Sam’s rewriting of the NASA flack’s pap on the spot). Ooh, I know: Sam writing and rewriting the note instead of going out with Mallory: “I just want to nail this.”
One that comes to mind is the episode where Enterprise’s Dr. Floxx comes in and wants all the world maps in America changed because it underrepresents Africa. C.J. is forced to meet with them and initially dismisses them as looneys, but gets more and more convinced that they have a legitimate concern.
YES! That whole episode was great. It had several quirky threads going.
The second time President Bartlett meets Ainsley Hayes (although, the first time he meets her and she’s dancing to Eydie Gormé is also a good moment)… President Bartlett asks her if she likes working at The White House and she says that she does. His follow up question is “Is your father proud of you?”
I love that moment, that he’s intuitive enough to recognize that she would be someone to highly prize her own father’s esteem and the empathetic generousness in presenting her with an opportunity to affirm it with pride.
And when she answers, just a simple and quiet “Yes, he is.”
She just beams. One of the single best moments of acting on the entire show. Just the way she says “Yes, he is” tells us so much about who she is, where her values lie, and it makes us root for her. Just such a simple exchange, done so beautifully.
I just watched the episode where they’re having an all-night poker session and someone shoots at the press briefing room, where CJ, Will, and Toby are. There were other bombings and assassinations around the world, and while Bartlet and Leo are in the Oval Office trying to get a spy plane back from Russia, the decision is made to crash the West Wing.
Jed says something to the effect of, “Ain’t no way you’re keeping Charlie out of here” and sure enough, Charlie come charging past the Secret Service (followed by Debbie.)
Little lovely moments about the relationships. Sure, he’s the most powerful man in the world, but he has the loyalty and respect and love of those who work under him.
Oh, and the scene where CJ successfully keeps the press away from a talk Toby is supposed to have with folks protesting the World Bank. When Toby confirms she’s kept the cameras away (wouldn’t work now in the world of cell phones) and she says, “You want to do me on the table right now, don’t you?”
He murmurs, “When don’t I?”
Hee hee hee.
I just can’t pick one scene from West Wing. I enjoyed the way once Ainsley gets started, she just goes on until she winds down (example, her hiring interview with Leo). I liked Danny, CJ, and Gail the Goldfish and the way the set dresser changed Gail’s bowl each episode. I liked when Abby had the orchestra play “Oh Canada” for Donna to Jed’s great surprise and feigned outrage. I liked when Jed shot down the Christian delegation and the Dr. Laura. And Sam was good at the occasional twisting of the knife. I liked that Mrs. Laningham had no compunctions about shooting ANYBODY down, including Jed, and her showing approval by deciding who got to get a cookie. I liked the father/son relationship between Jeb and Charlie. I did think they stretched out the Tracy/Hepburn thing between Josh and Donna way too long. I liked the mutual respect/friendship that developed between Jeb and Fitz. And I loved it when after CJ ascended to Chief of Staff, Josh, then Toby, and then Jeb submitted their resignations to her. Among other scenes I enjoyed.
Oh, for the record, Jeb got the 1st Commandment somewhat wrong, though maybe the Catholic version is just different than the Jewish version. I learned it as “I am the Lord, thy God, who brought the out of the land of Egypt, out of the house of bondage. Thou shalt have no other Gods before me.”
I have to downvote the scene where Bartlet pwns Dr Laura, because Sorkin pretty much lifted it verbatim from an internet meme going around at the time.
I like the scene where Sam gets ripped on TV by Ainsley Hayes. Cut to Josh and Toby: “Sam’s getting beat up by a girl” “I’ll get the popcorn.”
A bit of really powerful dialog that has always stayed with me…
When Bartlet has been shot, is in surgery, and Leo is assessing the situation:
Leo: How do we communicate with Iraq?
Somebody: The King of Jordan has been helpful in the past.
Leo: Good. Let him know this is not a good day to mess with us.
I don’t know…sometimes Sorkin’s misogyny gets a little wearing. Both CJ and Ainsley sat in wet paint during the SOTU after party (I think that’s what it was) despite the wet paint sign. None of the men were dumb enough to do that.
It would have been funnier to say, “Sam’s getting beat up by a Republican.”