Here are some quotes that i have found on the web from Vivianreed.net/BMW and imdb.com on Boy Meets World. They are from various seasons. Please keep checking back for more :) also added some quotes from the show of my own :)

Cory: "I'm guessing it's either 'yes' or 'no,' but we both know how well I do on multiple choice."

Cory: "Sometimes I can't hold my breath long enough to get down to where Mr. Feeny likes to swim."

Cory (real cool-like): "Over here, dad. Havin' a drink with Mr. Feeny."

Cory: "It's hard to imagine you as a boy. Did your parents call you Mr. Feeny?"

Cory: "Shawn and I have another project we're working on."
Topanga: "Really? What is it?"
Shawn: "Well, you know how those dolphins get caught in the tuna nets?"
Topanga: "Yeah?"
Shawn: "It's got nothin' to do with that."

(Cory has taken on the small part of a sphere carrier in the school play Hamlet. He is talking to another boy, who is also a sphere carrier)
Cory: "Live your part. Make it your own."
Boy: "Okay"
(Cory looks at the boy puzzled as he leaves his place on the stage and bursts Shawn's costume with his sphere. Shawn pushes the boy, the whole stage gets into a fight)
Cory: "Ah Shakesphere as it was meant to be"
(Cory pushes everyone off stage and dances)
This quote was submitted by me :)

Shawn: "Tell me something. How do you ask a girl out?"
Cory: "Simple. You open the door and say, 'Get out, you're bothering me.'"
Shawn: "No, like, on a date."
Cory: "Well, Eric uses the shotgun approach. He just dials random numbers until he hears the word 'yes.'"
Shawn: "Sounds like a lot of work."
Cory: "Yes. And, after all that, what have you got? A girl! What's the point?"

(Shawn and cory start a class strike)
Cory: (singing) "Look fo the union label... (Shawn joins in) If you are buying that coat, dress or blouse. Remember somewhere our union's sewing, our wage's going to feed the kids and run the house."
.... Later on... (In the same rythem as before) "Look for the union label... is anybody behind you my Shawn?"
Shawn: (singing) "I gotta tell you... there's no one with us... we're all alone here... i'm gonna bail..."
Cory: "You'd better not"
Shawn: "Oh yes i am."
Cory: "No no no"
Shawn: "Yes, Yes, yes"
(This quote was made by webmaster)

(Shawn and Cory are starting a student union strike)
Cory: "What are we?"
Everyone: "We are kings."
Cory: "And what do kings say?"
Everyone: "Umm.."
Cory: "They say... no more macaroni..."
Everyone: "No more macaroni"
Cory: "We want steak."
Everyone: "STEAK"!!!
Cory: "And what do we want with our steak?"
Shawn: "Macaroni"
Cory: "No Shawn... we dont like Macaroni."
Shawn: "Oh."
Cory: "And aside this... LOBSTER!"
(Submitted by webmaster)

(later on... at the same strike)
Mr. Feeny: The entire football season...
Shawn: Uh-oh
Mr. Feeny: CANCELLED!
Shawn: But-but that means...
Mr. Feeny: Yes, Mr. Hunter. NO CHEERLEADERS!
Shawn: NOOOOOOOOOOOOOOOOOOOOOOOO!!!!!!!
Cory: Shawn, this is a strike, we have to be willing to make sacrifices
Shawn: But he's taking away my girls. WHY DON'T WE JUST SACRIFICE YOU??????!!!!!!!!!!!

(Mr. Feeny has sent Mr. Turner's students back to class after Shawn and Cory walked out of school on strike.)
Mr. Turner: What about Hunter and Matthews?
Mr. Feeny: Ah, for those two, I shall have to go nuclear.
Mr. Turner: What does that mean?
Mr. Feeny: I shall call their mommies.

(A father of a bride wants cory to marry his daughter but Cory says he isnt interested...)
Cory: ... Or your daughter
(bride comes out)
Cory: HOYEEE...
Later on...
Shawn: HOYEEE....
Cory: You just saw the bride?
Shawn: Oooh yeyah...

(In future)
Rachael(Texas Accent):You mean ya'll didn't stay friends.
Cory:Well,our marrige counsler says we're doing great.
Topanga:CORY!
Eric:I married a moose.
Takes out a picture.
Eric:We don't need counsling.

(In future)
Eric:Feeny!
Mr.Feeny looks at him.
Eric:Fe-he-he(coughs)
Mr.Feeny pats his back.
Eric:Woah,I can't do it anymore

Cory: "My kindergarden teacher was Mr. Feeny. In fact, he has been my teacher for every year of my life...ain't that somethin'?

Cory: "You're Stan?! Stan the plumber man?!"
Stan: "If I can't flush it..."
Cory: "No one CAN!!!!"

Shawn: "Take the money."
Cory: "But I love Topanga."
Shawn: "We all do. Take the money."

(Cory's dorm room. Cory watches the tape of Shawn and Topanga kissing)
Cory: Oh, that's right. Kiss him again, yo little... Oh, you hurt me so bad. And you, you best friend gigalo homewrecker. Why don't you take her back to your tornado invested trailer park!!! Aah! (Rips apart his night shirt) TOPANGA!
Isaac, his neighbor in the next room hears him.
Isaac: (OS) Shut up!
Cory: You, shut up!
Isaac: No, you shut up!
Cory: No, you shut up!
Isaac: No, you!
Cory: You shut up first!
Isaac: No, you!
Cory: No, you! Come on! You want a piece of me? I'm not going anywhere! Come on!
His door is broken down and Cory finds himself facing a large tough guy.
Cory: (sounding similar to Elmer Fudd) Hewwo.

Eric: Yeah! We'll wait here a hundred years if we have to.
Jack: Yeah.
Flash forward to "A HUNDRED YEARS LATER." Eric and Jack are now skeletons holding pies.
Rachel: I'll be out in a minute.