Harold and Maude, and as others have said, A Christmas story, and for Thanksgiving, no one has mentioned Planes, Trains, and Automobiles. For old movies, aka TCM, I have fallen in love with Dinner for Eight, and My Man Godfrey.
Then there was one called Adventures in Babysitting years ago. There was one scene in the middle that was especially hilarious. The babysitter with her charges is trying to escape from the mob/drug gang/bad people, who are trying to kill them for the info they accidentally have acquired. She runs into a club and winds up going through the stage door and appears abruptly on stage with the band. Tries to excuse herself and leave, and the band leader says, "Nobody gets out of here without singin' the blues." So she improvises a "Babysitting Blues," and the crowd is really into it. The bad guys are there but can't get to them through their admirers. It was awesome.
Any of the Marx Brothers movies
The Bird Cage
The Producers (original 1960s version)
Little Miss Sunshine
Big Trouble (very good rendition of the book, but the book is still better)
Everything on Sannois's list.
Moonstruck...didn't realize so many others also love and quote this movie! I ADORE it. Cher so very much earned the hell out of that Oscar!
Adding on to Young Frankenstein (Mel Brooks' BEST movie) I need to add in (from Mr Brooks) Robinhood: Men In Tights. Spaceballs. Well, most everything but I love those 3 the best!
Princess Bride...most definitely!
Monty Python Holy Grail. Life Of Brian.
Loved my Big Fat Greek Wedding....mainly because I worked in the restaurant business for ages and had scads of Greek friends, coworkers and bosses. And that movie was pretty spot on!
And there's a smaller movie that was comedy GOLD: I Love You To Death. If you love this list, you'll love that movie if you haven't seen it yet. Entire brilliant freaking cast. Tracey Ulman and Kevin Kline as wife and cheating husband that she tries to kill. Laughed til I cried.
Airplane. Naked Gun. Both riots!
Fargo...but to this day I'm still not sure if that was supposed to be a dark comedy or not. Either way, I thought it was fantastic and hilarious. The accents...Buscemi in a woodchipper...OMG!
My entire family very often quotes Princess Bride, Ghostbusters, Holy Grail, Moonstruck, Men In Tights, Spaceballs and Young Frankenstein.
And I also often repeat a line from another Brooks classic History Of The World...the immortal, gorgeous and talented Madeline Kahn...whenever I'm driving around here. In my bouncy truck on our lumpy-as-hell roads...I often mutter the first line in this scene: http://www.youtube.com/watch?v=1csMoLgTMk0
You jump in the saddle,
Hold onto the bridle!
Jump in the line!
I watch "The Blues Brothers" about every 6 months or so as part of a good mental health regimen.
It's just the greatest, funniest, smartest comedy ever, and I am not a fan of most comedies. Can you imagine trying to make such a movie in this day and age? Neither can I.
Plus "I hate Illinois Nazis." "Orange whip? Orange whip? Gimmed three orange whips." Plus "I'd like to thank the representatives of Illinois' law enforcement community for coming tonight."
"Best In Show" is the only other comedy that immediately comes to mind - "bleeeeeeeeeeeeeessssssssss the terriers!"
Even though there are a few key scenes that are unwatchable due to being downright scatalogical and depraved, there were some really funny scenes in "Bridesmaids." And none of them included Melissa McCarthy (I'm not a fan).
I'm thinking of the fantastic weird dialogue between Kristen Wigg (Annie) and Jill Clayburgh as her cringe-inducing but caring mother, and the sweet banter between Annie and the handsome Irish cop outside the mini-mart and when he takes her out to use the speed radar.
Also the scene at the engagement party where Annie trys to one-up the snobby bridesmaid to prove that she's been friends with the bride the longest - classic.
Comedy is so difficult - to me the best comedies are when an actor/actress reaches that fine balance between creating empathy/sympathy for a character which then allows the audience to laugh as their all-too-human foibles are exposed.
I hate films (and to me, most of the current so-called "comedies" coming out of H'wood fall into this category) that abjectly humiliate the characters. It's just uncomfortable to watch rather than funny.
A few more:
"Legally Blonde" - Reese Witherspoon is a comedic genius, throw in her turn as Tracy Flick in "Election", too.
Most of Ben Stiller's films - "Meet the Parents", "Zoolander", even "Starsky and Hutch." He's just brilliant, especially his classic pairings with Owen Wilson.
Vince Vaughn in "Swingers" and "The Break Up" - I'm overall not a fan of the latter film or Jennifer Aniston but his scenes with his brothers as they run their tour-guide business in Chicago is hilarious. And "Swingers" still holds up some 20 years later and is hilarious.
It's black and white and artsy but when Roberto Begnini (sp?) starts chanting "I scream, you scream, we all scream for ice cream" in Jim Jarmusch's "Down By Law" I fall on the floor laughing.
Larksmom, that is one of the funniest lines in movie history. Cher was so good in that role!
I agree with so many on the lists but I have to add:
It Happened One Night (oldie but goodie)