As disappointing as the Baldwin-Basinger remake of The Getaway was, I was really impressed with the way Thick as Thieves (1998)came together. It’s almost a comedy, but Andre Braugher and Bruce Greenwood have some really good lines and Baldwin is cool, too. I have watched it at least three times and like it better each time.
I don’t know any other way to do this, so here goes:
Technically, so is Heist, mentioned way above. The heist is buried about two levels deep in cons.
Yeah, but in the Mamet, the con pretends to be a heist. There isn’t even a “fake” heist in The Sting
Yeah, that’s why I spoiler boxed it. I wanted to say “Spoiler for movie x,” but even saying which movie I was referring to would spoil it, given what I was responding to.
Thanks for all the awesome suggestions, everyone. Looks like we’ll have plenty of movie night fodder… at this rate, enough to get us through the summer, at the very least. 
Oh, and as far as recommendations go, please feel free to recommend con jobs as well… the way I see it, the line between heist and con can get a little blurry sometimes, and some of the best heist movies involve an element of con job anyways (especially when there’s a double-cross along the way).
Zsofia, I happen to like fun fluffy movies, so I really enjoyed Oceans Eleven (and, to a lesser degree, the two sequels)… but The Boy, he prefers his movies a little weightier. Hence the ask for more serious and gritty recommendations.
Topkapi definitely deserves a mention.
I’m unsure if it’s easily available, but you might look for The Hot Rock. IIRC, it was an early-70s picture about a jewel heist. It leans toward the comedic in spots, but I recall it as being pretty good.
Another from approximately the same time that might be a little more difficult to locate is They Came To Rob Las Vegas. I don’t remember much about this one, but I do recall a supposedly-impregnable armored car transporting millions that the gang was trying to … well, heist.
Indeed, with Robert Redford, George Segal, and Zero Mostel, that film is indeed quite (pardon the pun) a Gem! 
And remember: Afghanistan Banana Stand
Good job someone already did then!
I really enjoyed the original (1977) Fun With Dick and Jane.
I also enjoyed the 1971 The Heist.
Going in Style and Quick Change are both fun, though the heists are over pretty quick in both, IIRC.
Sleuth (The original, with Michael Caine, not the remake with, uh, Michael Caine.)
Missed the con job addendum.
Great con flicks not yet mentioned: House of Games and The Spanish Prisoner.
(Yes, Mamet seems to have gotten quite the bug there for a while, didn’t he?)
Ronin is a pretty straightforward heist movie. Plot: bunch of guys try to steal a suitcase.
On the lighter side of heist movies, how about A Fish called Wanda? Plot: doesn’t really matter.
Rats - I actually thought I’d read the entire thread.
Sweet alien Jesus, how did it take 33 posts for someone to mention Wanda?
Diggstown is an okay heist/con movies (more con) with what may be the most satisfying ending to any movie ever.
Bottle Rocket is a great heist gone wrong movie.
I see they have a remake coming out this summer.
Cops & Robbers is an old favorite of mine. (Unfortunately it is only available in FF, not WS AFAIK.)
I love the Arkin/Falk movie The In-Laws.
I can also second (or third) Heist and offer another Mamet flick: Glengarry Glen Ross.
Glancing at my DVD shelves:
Dog Day Afternoon w/Al Pacino
The Freshman - w/Matthew Broderick, Marlon Brando - not so gritty con movie that will keep you guessing
Three Kings w/George Clooney, Ice Cube, Mark Wahlberg - sort of a heist/war movie
Reservoir Dogs w/Chris Penn, Harvey Keitel, etc. - Tarantino film involving a heist
Jackie Brown w/Pam Grier - Tarantino film involving a heist
Trainspotting w/Ewan McGregor - drugs, violence, and multiple heists
Formula 51 w/Samuel L. Jackson - fun caper flick
Lucky Number Slevin w/Josh Hartnett, Lucy Liu - fun caper flick
2 of Guy Ritchie’s movies, Lock, Stock and Two Smoking Barrels and Snatch are excellent caper movies.
And for last I saved Bowfinger (“The Con Is On”), which is better than you will believe until you see it for yourself and Jay & Silent Bob Strike Back, which isn’t about a heist, but one does figure into the story very prominently. I saved them for last because they are both (hilarious) comedies, not the gritty rough stuff that the OP asked for.