I asked Courtney as much and she suggested a few. We spent the next 10 or 20 minutes trying to come up with an answer. Right off the bat, she suggested "American Beauty" and "something by the Cohen brothers". Later, she added "Gross Pointe Blank", "Lost in Translation", and "that whole genre of movies" like "The Life Aquatic" and "Rushmore". I feebly suggested "The Lord of the Rings", though that's actually three (highly overrated) movies. Also, "Saving Private Ryan" (cheesy), "Saw" (dubious), "Charlie's Angels", "Down with Love", "Bend it Like Beckham" (pervert), and "one of those Hugh Grant movies".
Why did I suggest several movies that I don't particularly like? Look up the word "great". Try to forget the weak way we use the word most of the time. How was dinner? Great. How was your weekend? Great, how was yours? You owe money on your taxes. Greeeaaaat.
Define "great movie" as a movie that totally changed the landscape of film. Other movies copied it, maybe still do. You have watched it at least 4 times and will watch it many more times in your lifetime -- bonus points if you don't mind the fact. Maybe the film affected popular culture (music, fashion, language) in general. It probably was influential worldwide, not just in English speaking countries. And yeah, maybe it picked up a few Oscars too.
So while "Saw", "Scary Movie", and "American Pie" are not my cup of tea, I can still consider then for discussion. And dismiss them, along with every other film suggested so far.
When we couldn't come up with more strong contenders, we resorted to the Internet. Scanning through recent Oscar winners and a couple of best-films lists (there's actually a site that lists the lists), we could only come up with one more contender, "Fargo", which really just clarified Courtney's "something by the Cohen brothers" pick.
Films like "Boogie Nights" and "Magnolia" are certainly contenders. And they are influenced by "Pulp Fiction"; e.g., the casting of Burt Reynolds, Travolta-esque has-been.
As I was lying in bed this morning, I thought of another: "Toy Story". Today, computer animated feature films are commonplace. Did "Toy Story" usher in the era through its greatness? Or was it a technological inevitability? Probably a lot of the former and some of the latter. Going over my signs-of-greatness checklist, it's very close. I've certainly seen it many times. Not sure if I want to see it many more times. It broke new ground in animation, but not so much in other areas. I may change my mind, but today I say "Toy Story" is very close. The closest I can think of.
So has there been a great movie released since Pulp Fiction? The answer, sadly, no.
But I haven't seen "Borat" yet.
Update (written Jan 24, 2015): In the original comments section of my old website, three people voted for the "The Matrix" as a great movie. I completely agree. Several other movies each got one vote: "Bowling for Columbine", "Fahrenheit 9/11", "Being John Malkovich", "Adaptation", "Eternal Sunshine of the Spotless Mind", "Kill Bill" volumes 1 and 2, "Breaking the Waves", "Jackie Brown", "Run, Lola, Run", and "Point Break".