If you are looking for free, public domain, music online, look no further than IMSLP.

There is a ton of content here, but I was able to find some of the most popular pieces for the trombone that are public domain.

Ferdinand David Concertino

Camille Saint-Saëns Cavatine

Friedeblad Gräfe Concerto

Nikolai Rimsky Korsakov Concerto

Joseph Guy Ropartz Piece in Eb Minor

There is a ton of content to sift through here. If you find more of the significant works for trombone on IMSLP either leave the link in the comments, or email me the link.