“It means: Be advised. I’m mean, nasty and tired. I eat concertina wire and piss napalm and I can put a round in a flea’s ass at 200 meters. So why don’t you go hump somebody else’s leg, mutt face, before I push yours in.”
From “The Gauntlet”, the Eastwood character is commandeering an outlaw motorcycle gang leader’s motorcycle to get him and the witness he has in protective custody to court:
Outlaw Biker Guy - “That’s my bike man!”
Clint (with huge pistol shoved up Biker Guy’s Nose) - “This is my gun, Clyde”.
“My mistake. Four coffins.”
Little Bill Daggett: You’d be William Munny out of Missouri. Killer of women and children.
Will Munny: That’s right. I’ve killed women and children. I’ve killed just about everything that walks or crawled at one time or another. And I’m here to kill you, Little Bill, for what you did to Ned.
also
“All right, I’m coming out. Any man I see out there, I’m gonna shoot him. Any sumbitch takes a shot at me, I’m not only gonna kill him, but I’m gonna kill his wife, all his friends, and burn his damn house down.”
It’s "When you have to shoot, shoot, don’t talk. " and it was Eli Wallach’s character who said it.
Don’t know if it’s my favorite line, but it’s one of my favorite scenes:
“Give him a drink of water, goddamn it. Will you give him a drink of water, for Christ’s sake? We ain’t gonna shoot.” - Unforgiven
In the beginning of “Sudden Impact,” a young punk gets off in court because Dirty Harry has somehow screwed up procedure. Then the punk and his lawyer end up sharing an elevator with Harry on the way out of the courthouse. The punk mouths off, and Harry delivers this great monologue:
“Listen, punk. To me you’re nothin’ but dogshit, you understand? And a lot of things can happen to dogshit. It can be scraped up with a shovel off the ground. It can dry up and blow away in the wind. Or it can be stepped on and squashed. So take my advice and be careful where the dog shits ya!”
Oh, and another popular favourite:
Harry Callahan: Well, when an adult male is chasing a female with intent to commit rape, I shoot the bastard. That’s my policy.
The Mayor: Intent? How did you establish that?
Harry Callahan: When a naked man is chasing a woman through an alley with a butcher’s knife and a hard-on, I figure he isn’t out collecting for the Red Cross!
My son does quote it correctly. septimus is the one with creeping senility. 
From White Hunter, Black Heart:
“You, madam, are the - Well, you know the rest.”
Doesn’t make much sense with the scene (third quote).
The actual scene is here (good part a bout 2/3 through).
Two from High Plains Drifter
Somebody left the door open and the wrong dogs came home.
You’re going to look pretty silly with that knife sticking out of your ass.
And another exchange from Two Mules for Sister Sara:
Sara: [Wants Hogan to bury the three men he’s just killed] Do you have a shovel?
Hogan: Sister, raise your eyes to heaven.
[They both look up at the sky, to see vultures circling overhead]
Hogan: Now are they or are they not God’s creatures?
Sara: Of course they are.
Hogan: Well, why do you want to rob them of all this convenient nourishment?
Stranger
From “Sudden Impact”
Callahan alone disrupts a robbery in a diner: “Well, we’re not just gonna let you walk outta here.”
Robber: “Who’s ‘we’, sucka?”
Callahan: “Smith, Wesson, and me…”
Callahan’s Partner, on the effectiveness of a 12-gauge: “Not bad? Not bad my ass. You gotta strain the remains for the fingerprints!”
Callahan: “Well this here’s the .44 magnum auto-mag. It fires a 300 grain cartridge, and when properly used, it removes the fingerprints.”
You left out the best part. If I remember correctly, the criminal gives up, then says:
“I gots to know.” So Harry puts the gun back up to the criminal’s head and pulls the trigger, but the gun is empty.
Heartbreak Ridge, after his character is wounded (and is being tended to by one of his men).
High Plains Drifter
“To your feet, ma’am.
They’re almost as big as your mouth.”
Another from Unforgiven:
Little Bill Daggett: Well, sir, you are a cowardly son of a bitch! You just shot an unarmed man!
Will Munny: Well, he should have armed himself if he’s going to decorate his saloon with my friend.
“strip the Caddie Clyde” - talking to his Orangutan in Any Which Way but Loose.
“God this stuff isn’t getting to me - the shootings, the knifings, the beatings. Old ladies being bashed in the head for their social security checks. Nah that doesn’t bother me. But you know what does bother me? You know what makes me really sick to my stomach? It’s watching you stuff your face with those hotdogs! Nobody - I mean nobody puts ketchup on a hot dog!”
I think the exact text is:
“Right turn, Clyde.”
(And it’s either “Every Which Way but Loose” or “Any Which Way You Can”.)