Definitely Take Five. I know dick-all about jazz, but I know that song.
The Pink Panther by Henry Mancini is the best known, and for some of the wrong reasons. It was the theme for the original movie, where the cartoon character was introduced in the credits. Three or four (?) sequels all had the same song. A brief Pink Panther animated kids’ show made it known to a generation of kids. The cartoon character and theme were used for many years to advertise fiberglass building insulation and shingles.
Now, besides all that, it’s a very cool song, with flashy dynamic changes through the course of it. 
Does someone have a definition we can go by? I think “jazz” is a lot like “rock” in people’s minds…it’s a catch-all term. Can jazz be more narrowly defined? Are there elements of jazz that don’t spill over into other genres?
“Take 5” was what I thought of before opening the OP, but to throw another one out there, Herbie Hancock’s “Cantaloupe Island” is probably readily recognizable, although more from US3’s “Cantaloop” than the original 1964 Blue Note recording.
This one definitely gets my vote. It’s the one that I thought of when I saw the thread title, before opening the thread. Some of the others listed may be well-known among jazz fans, but among the general public, not so much.
The jazz song that’s best known among non-jazz fans would almost have to be one that’s known from its use in a popular movie or TV show. Or maybe one that was a big crossover hit on the pop charts, but it’s been a while since we’ve even had such things.
Either *Pink Panther *or Linus and Lucy (Charlie Brown / Peanuts Theme). You can’t beat the “1-2 punch” of radio/records AND television/movies when it comes to boosting a song’s popularity!
Might Herb Alpert’s “Rise” deserve an honorable mention?
I think it gets in just under the wire, but how about Henry Mancini’s Theme from Peter Gunn?
Good one.
Both “Theme from Peter Gunn” and “Rise” are songs you heard a lot more 20-30 years ago than you do today.
I’ve heard at least one cover of the Mr. Roger’s song It’s You I Like. That’s got to be highly recognizable. I don’t know who sings it, or even if there have been multiple covers.
Depends on how broadly you define jazz. Does Chuck Mangione count? If so, then Feels So Good probably makes the list of most recognizable jazz numbers.
I’ll throw in my vote for “Take Five” and “Girl from Ipanema.”
I listen to classical music almost exclusively, and “Take 5” is the only jazz piece I know by name, solely for its meter and IIRC a local tv station used it between segments of late-night movies when I was much younger. I don’t know any of the others mentioned except the Guaraldi and Mancini stuff, but are they now considered actual jazz or more in the direction of easy listening? Not that it makes a difference to me.
A cheap chess game for my Commodore 64 used Take Five for sound effects when a piece moved. I didn’t recognize it until I became interested in Jazz 20 years later and bought a Dave Brubeck CD. 
Does the Frasier theme count as a “jazz song”? other jazzy TV themes?
I think the Miles Davis classic album “Kind of Blue” is still the biggest selling jazz album of all time – but I’m betting most people couldn’t tell you what was on it, even if they have a copy.
From non-musicians, hands down, Take Five and The Pink Panther; I’ve had people tell me the Brubeck album with Take Five is the only jazz album they own. (I dunno who’s buying all those copies of “Kind of Blue.” (Though it’s still pretty damn good nearly 50 years later.)
I would also throw in some of the trad tunes, most notably When the Saints Go Marching In. EVERYBODY knows Saints; it’s the Happy Birthday of Dixieland. I can play it in every key . . . . by heart. You just know it.
That would be me… Fifty years? I had no idea. He is wearing a tie on the album covers.
So what?
Sorry, couldn’t resist.
Another nomination for the Brubeck standard, since it satisfies a more stringent definition of “jazz” (does not include Kenny G.) and might be “best known” in a sampling older than the average Doper.