My list:

1. Harold! ("Jealous? His name is Herbert. I talk to him when I get lonely. Hehe, just kiddin'. His name is Bob!")
EDIT: 2. Enclave Drill Sergeant. ("The truth is, that you have lost expensive army issue EQUIPMENT, and that's coming out of your PAYYY, and you willstayinthisguardpostuntilyouare fiiiiiiivehundredandtenyearsold, which is the number of years it will take for you to pay Mk.II Power Combat Armor!")
3. Melting enemies after tasting some plasma

1.) Acquiring the last part for the Chrysalis Motors Highwayman car... Then joy riding around the map. =] The music was also awesome. http://www.youtube.com/watch?v=eB_Safe9QAs&feature=related
2.) Probably other memorable experience was visiting the bombed out radioactive vault and not understanding lethal radiation doses... And dying after traveling one grid in any direction on the world map. LOL!
3.) Getting the Pancor shotgun and blasting the torso away on an enemy at point blank range.

I've only played Fallout 2 (other than a few minutes of FO3 at a friend's house - and I just got FO3 but I'm still working on my gaming rig):
1) Grampy Bone!
2) Going on a killing spree in the Den.
3) In Enclave base, talking to the robotic dog. He says that he can't talk to me, becuase I'm not his master. Then I pickpocket and put some C4 in his master's pocket and blow him up without any reputation hit. Then the dog says "Are you my new master?" For some reason I find that hilarious.

Only play Fallout 1 but here its goes:
1. Beth and Sid: Funny couple
2. Dogmeat: Best joinable character there is
3. .223 Pistol: Dam this pistol is sixy!

1. Getting caught naked with Davin by his father, then having him make a speech about how he understands his son's choice, that he always thought he was this way and then finally forcing you to marry him while your character says things like : "But...wait!" "Let me explain..." "No that's not..." <=== That sequence made me laugh. A lot.

2. Arriving in New Reno for the first time. Discovering how dangerous it is if you are a goody two shoes, or how nice and awesome it is if you are an evil person, especially a slaver addicted to jet (Which is my current character)
New Reno has the best price on Jet!

3. Dialogue. Simply put. One of the best I've seen.

1) The most creative and intruiging endboss ever in a game: The Master. Dialogue with this guy was amazing.
2) The "Good, Bad and the Ugly" reference in Fallout 2 on Golgotha: "There are two kinds of people in this world, Lloyd, people with loaded guns and people that dig."
3) Mocking Gizmo in Junktown over and over again: "Izo, get me a set of kneecaps."

I agree.
I have a special savegame in FO1 which is used to play the Master over and over again. It's so awesome.

"Who else? The ghouls? Please. Normals? They brought nuclear death to us all! This will be age of Mutants, mutants!"