Mine was the talking tree in the enchanted forestt. Especially at the end where you go back to talk to him and he just says "Yeah...I'm kind of freaking out right now so could you maybe leave me alone..."

I don't remember word by word how it went, but here goes. 
Talking tree: "DeathSpank" 
DeathSpank: "You have heard of me?" 
Talking Tree: "The rain and the wind whispers your name" 
DeathSpank: "Finally!"

Mine is with the fisherman it went something like this: 
Deathspank: "Why do the Greems hate you so much?"
Fisherman: "I eat their young. Makes them awfully cranky!"
Deathspank: "Ok..."

Maybe one of my favorite moments was when you met the brat in the Demon Caves. 
"They say I'm not supposed to talk to strangers" 
"But I'm not a stranger... I'm DeathSpank! Now get in the bag" 
It just sounded pretty hilarious, although the joke kinda overstayed its welcome when you had to bring her candy. 
 
I also enjoyed Freen's goodbye comment: "Make sure to tell your friends that you've gotten Felt by Freen". lol.  
 
Oh, and when I picked up a flyer that said something along the lines of "Friendly reminder from the Leprechaun Council of Family Values: Snitches get stiches". At that point I hadn't even met a single leprechaun yet, so it seemed absurdly funny.
 
But the one that really cracked me up was making conversation with Ick and Badger in the museum. When they start talking about some movie, and DeathSpank ends up concluding 'I'll just bittorrent it'. I also really liked the relationship DeathSpank had with those two. Very fun indeed.

I like the brat too...especially when she demands a pony and DeathSpank replies with something along the lines of, "okay I'll get you a pony but it's gonna be an ugly one!"
 
I giggled a little too when I got a poop hammer

So far, everything to do with Rich Cabin and his "Cabin's for the Rich". There's something about his voice actor I find hilarious. Eubrich is pretty funny as well.

I loved when you first talked to the Guy in Pluckmuckle with the apple name.  
Deathspank: "You parents must've loved there apples." 
Guy: "Nope, they hated them." 
Deathspank: "Ok..."

Eubrick was one of the funniest characters imo. Freen was funny but he didn't have as much dialogue as Eubrick. I was always laughing at the lines. My favorite was either "I once slain a dragon! Well I didn't really slay it and it wasn't technically a dragon. What I meant to say is that I once kicked a cat!" or the dialogue when Deathspank had to finish up Eubrick's quests.