The Cartoon Quote Game...

Almost perfectly correct, this is the I Want Song from Jack Skellington, supreme ruler of Hallowe'entown from Tim Burton's The Nightmare Before Christmas. For the record, it's "shriek," not "schreek."

Oops. My autocorrect wasn't working.

"He's not drunk, Mom, he's just eccentric."

Coraline Jones, from "Coraline."

Yep, it's Coraline.

BTW, OUB. The official name of Jack's song is "Jack's Lament." (Not to nitpick or anything )

Thanks, Salty. Now for a good one:

"Murray, Aykroyd, and Ramis? What's that, a law firm?"

Oh, that's not nitpicking. My fault for not using a hyperlink to TV Tropes' I Want Song, where a character expresses their motivation / objective / unrequited love in a song, as a way to give the audience a peek at what goes on inside that character's head. Fixed post facto.

Ah, like a stage monologue in the form of a song. I see.

As for the quote it's Winston Zeddemore, from The Real Ghostbusters.

Saltyboot, you've scored again. Good job. . Can't wait to see the next quote.

And quote I shall.

"I met her today in the maze. Her name is Billie. She's of simple folk, fair and true."

"You mean she's stupid?"

I had no trouble finding the answer, but now it's time someone else had a turn.

While I don't recognize the quote per se, I do recognize the stealth pun within it: "Her name is Billie." Alternately spelled Billy. "I met her today in the maze." Operative word here is maze, a homophone to Mays. Billy + Mays = Billy Mays, the late exuberant pitchman for Oxy Clean. This smells like a Fox animated series, methinks.

Sorry OUB, but you're way off.
The quote is from a series though. From the 1990s.

I had to look this one up myself.
It's from Animaniacs, but it's a Pinky and the Brain short.
Brain is saying the first part, Pinky is actually saying the second bit.

Yes, that's it. It's the Brain, and Pinky.

"Mary had a little lamb, BUT I ATE IT!"

Just found it. It's the possessed duck woman from "Daffy Duck's Quackbusters."

Correct. The short is also a standalone called "The Duxorcist." I used to see it a lot as a child on ABC's Bugs Bunny and Tweety Show.

Thanks, Glowworm. Now for a perfect set of quotes:

"I'm chocolate."

"I'm strawberry."

Hint: Their cereals, along with three others, are now a Halloween tradition.

Well then, these would have to be General Mills' Count Chocula and Franken Berry, two "rival" cereals in a parallel vein to Quisp / Quake. They later added Boo Berry and Fruit Brute, but they didn't last long.