Guessin’ just off the top of my head I’d venture Green Onions.
The oldest recording on my iPod right now is Call Me Burroughs by William S. Burroughs, which came out in 1965.
Edouard Leon-Scott’s photoautograph from 1860. Both the original digitization (that was thought to be his daughter because it was speeded up) and the corrected one (Leon-Scott himself).
I win.
Just listened to his Au Clair de la Lune from 1860. He really didn’t hit the right levels, his EQ is all over the place. 
That’s pretty impressive for the fact that it still exists.
I downloaded some Lead Belly from archive.org to use with Fallout 3; as for my iPod, probably Glenn Miller stuff from the late '30s.
Well, if we’re talking any recordings, there’s the 20+ wax cylinders with the Edison Gramaphone in the attic. I have no idea what to do with them.
There’s a place out west that’ll MP3 them, but it’s destructive. Rrrroughly 1919, I think.
IIRC Theres one place that uses laser to do it. They specialize iin cylinder preservation.
I was going to mention some songs I have from the 1950’s (Rocket 88 probably being the oldest), but this reminds me that I also have Who’s on First?. I believe the version I have was recorded sometime in the 1940’s.
George J. Gaskin singing “After the Ball Is Over,” recorded in 1897. I also have 200+ songs from the 1920s and '30s. I love old-time popular music. 
On second thought, I think I missed the point of the OP. While Who’s on First? is the oldest thing in my collection, it’s not the oldest thing on my MP3 player at the moment. That honour would belong to Rock Around the Clock by Bill Haley and His Comets.
Lydia the Tattooed Lady, from 1939.
The oldest song in my MP3 collection that has a recorded date on it? 1933. Popeye The Sailor Man. (agg-gag-gag-gag.)
I probably have older, but not with a date listed in the year section.
The oldest recording on my iPod is also the music file I’ve had the longest*: a Django Reinhardt piece (probably late '40s) that a friend sent to me over AIM my first year in college, 1998.
- –> Not counting tracks from CDs that I’ve reinstalled on newer computers.
Wow. Same year for me… and same album.
If I were to guess I’d have to say eithe r Constipation Blues by Screamin’ Jay Hawkins or Stan Freberg’s version of Banana Boat.
I think right now it’s the Benny Goodman recording of Sing, Sing, Sing.
Off the top of my head, I think my oldest is **Tom Dooley **by the Kingston Trio from 1958. Runner up would be Bobby Darin’s **Mack the Knife **from 1959.
I have several Annette Hanshaw compilations, as well as old Louis Armstrong, all from the 1920s. Oldest written, probably Hildegarde von Bingen.
I like colonial-era American music so I have some William Billings covers by the Boston Camerata, dating from 1780-1820 or so.
The oldest direct recording is from 1927, Helen Morgan singing “Bill” from the original SHOW BOAT. I have a couple of small comedy bits that are older, including “The Baseball Girl” from 1907.
Stuff from* Art Tatum Solo Masterpieces* all recorded between 1953 and 1955.