I’d think the Christopher Guest mockumentaries might fit the bill. Best in Show is my favorite.
My Cousin Vinny is hilarious and not too idiotic.
LOVED that movie!
Also loved The Wonder Boys.
Bullets Over Broadway
Lost in America
Parenthood
My Cousin Vinny
Planes, Trains and Automobiles
This Is Spinal Tap
Being There
Harold and Maude
Eating Raoul is kind of highbrow; excellent deadpan black-comedy parody of swinger culture and foodie culture.
Thirding The Fifth Element! It’s SF and it doesn’t take itself seriously at all, it’s all wide-eyed SRS BZNSS while they’re cracking up on the inside.
Hot Fuzz. Again, steely-eyed serious business with hilarity on the inside.
**Enchanted ** if you’re up for a gentle sendup of classic Disney princess movies. May be rather a bit girly for you though.
Galaxy Quest. Pure cheese comedy gold especially if you’re at all familiar with the ST franchise.
My netflix list is crying under the strain now. Thanks dopers!
This is the first time I’ve come across someone else that actually has seen and liked this movie! 
I’ll second L.A. Story and add Death at a Funeral. A good British farce by director Frank Oz.
I think Fargo has enough comedic moments to classify itself as a comedy, just my own personal opinion. You can really plug it into a few genres, however.
Also, Ghostbusters.
Men in Black
Any of the Monty Python movies.
I would suggest Murder by Death. It works on both a low and high level. If you are familiar with the detectives and mystery writers of old, it is a very literate comedy. If on the other hand, you don’t know any of that, it works as a very funny physical comedy. The wife and I saw it for the first time when it came out at a multiplex with a theater full of teenagers. They did not laugh at all at the highbrow stuff that had my wife and I on the floor. We laughed at the lowbrow stuff also. IOW we laughed pretty much nonstop.
Who wouldn’t love an exchange like this
Shaun of the Dead is by the same people who made *Hot Fuzz[i/], and they’re both very funny movies.
Withnail and I, though that might be a little wordy and gloomy for GF.
The Forty Year Old Virgin is a movie your GF would probably like and has enough smart dialog to keep you from pulling out your hair.
Australian Film “The Rage in Placid Lake”. Very funny, very smart and Rose Byrne is gorgeous.
And has no one mentioned “Zoolander”?
Woody Allen is an acquired taste, but he’s made some very highbrow comedies. Notably: ** Annie Hall**
Play It Again Sam
Sleeper
Everything You’ve Always Wanted To Know About Sex
But Were Afraid To Ask
Love And Death
Also, Blake Edwards has a tendency to “go over the top” when he directs comedies, but I enjoyed SOB and Victor/Victoria
“That man is dead, and all the doors are locked from the inside. That can only mean one thing. And I don’t know what it is.”
I assume you’ve also seen the follow-up (of a sort) The Cheap Detective.
Actually I don’t think I have, I will have to go find it.
Of the classics,
Harvey
The Philadelphia Story
The Thin Man (and sequels)
Arsenic and Old Lace
are favorites, along with already mentioned His Girl Friday
Ditto folks above who mentioned Sideways, Little Miss Sunshine, and The Wonder Boys (great satire on the academic world and on the writing world.)
An oldie but a goodie Kind hearts and coronets - very good black humour. For the same reasons I would second/whatever Clue.
The President’s Analyst
Adam’s Rib
Monkey Business
Desk Set
Bedazzled (Cook and Moore version)
The Producers
The Taming of the Shrew (Taylor, Burton)
Much Ado About Nothing (Branagh)
Yes, I’m a broken record, but dammit it’s still grand fun:
Those Magnificent Men in Their Flying Machines or How I Flew from London to Paris in 25 Hours and 11 Minutes
Similar, thematically, is the Tony Curtis movie The Great Race.
Both of which feature a scheming villain with wonderfully Rube Goldberg-ish plots.
I tend to think that Cary Grant did a lot of wonderfully witty comedies that have stood very well with time. I have issues with Bringing Up Baby, but it’s already been mentioned once in this thread.
Personally, I love his:
Father Goose
People Will Talk
Arsenic and Old Lace
I Was a Male War Bride
His Girl Friday
Unless you’re a huge Cary Grant or Myrna Loy fan, though, do yourself the favor of avoiding The Bachelor and the Bobby-Soxer. Trust me on this. There’s a reason it’s not available on DVD.