Thanks to the latest posters. I’m adding your suggestions to my list.
I second that. But then, if Fields just walks onto the screen, I start cracking up.
Some are over-the-top funny, some just chucklers, but almost all good: Mystery Science Theater 3000
Harvey. What’s not to love about a six-foot invisible giant rabbit?
I always liked Arsenic and Old Lace. The nutty brother who thought he was Teddy Roosevelt always cracked me up.
My all-time favorite dumb/funny movie: Strange Brew. That movie was what let me and my S.O. know that we had something in common.
Two that haven’t mentioned:
The Ruling Class - Peter O’Toole thinks he’s Jesus (banned in Chile!)
My Cousin Vinny - Joe Pesci may be better in comedies than mob movies. Marisa Tomei won an Oscar.
(And let me enthusiastically second Waiting for Guffman, Best in Show, and Meet the Parents. All superb.)
Life of Brian funniest movie ever made
Everything Monty Python.
This is Spinal Tap
**Southpark{/b]
Was the Royal Tenanbaums a comedy?
Oh And
The Castle
Muriels Wedding
are both hysterical.
Rosencrantz and Guildenstern are Dead
Brilliant, thoughtful, haunting, and side-splittingly hilarious, all at the same time.
And it’s not out on DVD yet! What the hell is wrong with the world?
Oh, and I wanted to plug a couple of recent Disney films that really surprised me by being genuinely funny:
The Emperor’s New Groove
and
Lilo and Stitch
Orgazmo, the only movie with a mormon-martial artist-porn star-super hero as its main character.
A third (or whatever) to the Marx Brothers films, especially Duck Soup, A Night at the Opera, Animal Crackers, and parts of A Day at the Races.
Also, I’ve yet to see a mention of Army of Darkness. Is it a great movie? No, but it’s a hell of a lot of fun. Bruce Campbell is great as Ash. “Hail to the king, baby.” 
Oh, and shame on everybody for not mentioning The Big Lebowski. Strange, but very funny and charming in its idiosyncrasy.
I’d like to add Woody Allen’s Sleeper which may be his funniest, and two of Alec Guiness’ rarely seen wonders, Kind Hearts and Coronets where Guiness plays about a dozen family members being killed off so a lowly, distant cousin can inherit the family fortune, and The Man in the White Suit where Guiness invents a fabric that won’t wear out or get dirty, much to the distress of management and labor (sorry, labour) who see the end of their industry.
And I want to second Duck Soup since it’s the funniest movie anybody ever made.
Actually, I put it as a comedy because I’m not sure what category it belongs in. It has hilarious moments, and it has harrowing, desolate moments.
Uh, you made me explain myself. Strike The Royal Tenenbaums. 
Marley - Of course - The Big Lebowski :smiley hitting head
More kudos for “Duck Soup”, 'Young Frankenstein", and especially (cuz it’s the one I had forgotten) “Amazon Women On The Moon”.
And a first mention (I believe) of Mel Brooks “Silent Movie”. It has two of the great comedy bits in it (Henny Youngman, and Sid Ceasar in the hospital), and how can you not like a silent movie with the only word spoken in it comes from the voicebox of Marcel Marceau?
Many of Steve Martin’s comedies:
The Jerk
Tranes, Planes, & Automobiles
The Man With Two Brains
The Lonely Guy
Roxanne
All of Me
L.A. Story
Father of the Bride
Parenthood
Dirty, Rotten Scoundrels
and more!
Dirty Work
Rat Race (The scene were John Lovitz, dressed like Hitler, crashes a WWII veterans get-together.)
No one has mentioned Super Troopers or Joe Dirt yet? My heart is broken.
What about The Goonies?
I’m an idiot, how dare I forget Joe Dirt “I got’s the poo on me.” One of the funniest lines ever.
My favorite part in Super Troopers is where the trooper is acting like he’s going at it with a bear. Classic.
Mr Blue Sky,
I can’t believe I actually found another person on this planet that has seen Gregory’s Girl. Very, very sweet movie.