Before jazz : Marches and brass bands

US Marine Band - The Liberty Bell (1894 historic recording) (buy)

US Marine Band - The Thunderer March (1896) (buy)

US Marine Band - Maple Leaf Rag (1906) (buy)

WC Handy - Yellow Dog Blues (buy) (1922)

Marches, as played by military or civilian brass bands, were very popular in the 19th century. Marches were very influential both to ragtime (see previous post) and to New Orleans jazz.
John Philip Sousa, "the march king", composed dozens of very popular pieces that were first recorded in the 1890's by the United States Marine Band, which he conducted from 1880 to 1892.

The tracks I posted are among the oldest musical recordings in the world, so don't test your brand new stereo with them.

You'll probably recognize the first one as Monty Python's Flying Circus Theme. The second one, more syncopated, "with its lead trumpets, supportive trombones, and piccolos winging arpeggios over the top" (to quote Kevin Whitehead in this very interesting essay at emusic), sounds more pre-jazz.
The United States Band, nicknamed "the President's own", played various styles of music for the White House, and weren't indifferent to the ragtime boom of the 1890s as their recording of "Maple Leaf Rag" from 1906 attests.

W.C. Handy, the so-called "father of the blues" (more the father of blues copyright, as Whitehead says), recorded with his band between 1917 and 1923, so a few years before King Oliver and the first black jazz bands did so.
He was one of the first to commercialize blues as sheet music. Before that, there was a certain gap between musicians who could read music and those who played the blues and "made up their own tunes" (I heard a great Bunk Johnson interview about that). It is the meeting of these musicians, and especially in New Orleans where creoles and blacks interacted, that gave birth to jazz. WC Handy's band plays with the discipline of a "reading" band, without swing, but his music, in a sense, is the last exit before jazz.