In my home, it’s immediately followed up by
“That’s… the worst goodbye ever. And, it’s from a movie.” – Zombieland
You’re thinking of this Churchill quote:
That reminds me, I frequently use my best Rocky the Flying Squirell voice to say, “But that trick never works!”
Which I then follow in my Bullwinkle voice, “Nothin’ up muh sleeve!”
And the full Tim Allen quote seems to be a mashup between Churchill and The Three Amigos. 
Jason Nesmith: As long as there is injustice, whenever a Targathian baby cries out, wherever a distress signal sounds among the stars, we’ll be there. This fine ship, this fine crew. Never give up… and never surrender.
Sorry if any have been mentioned upthread already.
Well, if it ain’t a mess, it’ll do 'till one comes along. No Country For Old Men
Hello, [name], what’s the rumpus? Miller’s Crossing
I was in the neighborhood, feelin’ daffy. Miller’s Crossing
[Not a movie] The wha . . . .? Professor Farnsworth
“I’m your huckleberry.”
“Everything’s coming up Milhouse!”
Also, “… only a man’s who’s ass is narrow can fit down this hallway…”
And so he says to me, you got legs, baby, you’re everywhere…you’re all over the place! Yeah!
An object at rest, cannot be stopped!
Bad is good, baby! Down with government!
…Midnight Bomber – The Tick
D’OH!! - Homer Simpson
That’s gonna leave a mark. - Tommy Boy
You’ll shoot your eye out! - A Christmas Story
I double-dog dare ya! No, I TRIPLE-dog dare ya!! - A Christmas Story
Stay on target… - Star Wars
Can we shoot them? - Fiona on Burn Notice
“Close, Stoneberg, veeerrry close.” My Favorite Year
“You gotta be fucking kidding me.” *The Thing *
“It’s my duty to please that booty.”
–Sam Jackson, Shaft
“Embrace the mystery” from A Serious Man. I use it every time someone asks me to explain some idiotic statement or occurence. “What kind of a-hole jogger cops an attitude because the streets aren’t perfectly clear during rush hour downtown?” “Embrace the mystery.”
“RAMMING SPEED” From Animal House
Useful just about anytime one object approaches another. Whether you are coming in for a hug or mopping the floor.
“[You have] chosen poorly.”. Indiana Jones and the Last Crusade - whenever my wife or I make a particularly boneheaded decision.
“I wrote it down so I don’t have to remember.”. Ibid.
“My cat’s breath smells like cat food!“ (Ralph Wiggam) used when somebody answering a question clearly has no idea about the subject.
I am continually referring to students in my Taekwondo classes as Grasshopper.
And I’ll quote Yoda, too:
“NO! Try not! Do or do not - there is no try!”
“Who the hell is interrupting my kung-fu?!” – Black Dynamite
Luckily, we live in an age of Caller ID so I can answer the phone like that when my wife calls 
Forgive me if these are upthread but I used both today;
‘This old thing? I only wear this when I don’t care HOW I look’ - Gloria Graham in Its A Wonderful Life wearing a spectacular outfit, and
‘What wanton hubris is this?!’ Tommy Lee Jones as the overly verbose lawyer in The Client.
MiM
A line I use from Stripes whenever someone says “I have a plan”: “Wonderful. Custer had a plan, too.”
“Did you say that, Carl? Wotta guy!” Anytime somebody says something grandiose.
“I’m not shhhhhimmying down anything!” A plan has been made and it’s a doozy.
“That’s not [whatever]! It’s kissing and jumping and drinking and humping!”
Another good quote movie is Cannonball Run.
“Don’t start with him.” i.e. Let’s not talk about that.
"Next time – METHODISTS!" A plan has gone badly and now I must kill you, in a spiritual sense.
“What is this crude interruption?” (self-explanatory)
Probably not quite the spirit of the original post, but I frequently say movie lines to myself (yes, out loud) for self-amusement; a current fave is from the Skipper in Bull Durham:
“God damn it, Ebby! You ‘bout to make your professional debut! There’re guys’d give their left nut to be where you are, and you’re leaving your fastball in the locker room with some piece o’ ass!”
It’s the way he pronounces “piece o’ ass” that kills me. No, I can’t explain it, either.
It struck me today. Not quite a movie line, but a classic nonetheless and one I use more often than I realised:
“Good thinking, 99!”