By definition, and etude is a piece of music composed to develop and cultivate techniques, skills, styles, concepts, etcetera. 

For many of today's aspiring trombonists, etudes are a critically under-illuminated part of the curriculum. Warm-ups, exercises, patterns, audition excerpts, ensemble parts, and concerto passages dominate the regimen. Many - especially symphonic - trombonists rarely play a whole piece of music! There is a wealth of etude literature available to cultivate almost any style, technique, or further aspect trombone playing. I encourage all to explore that repertoire and its benefits, and to tap into the motivation and momentum that this musical pursuit can provide.

Etudes are a link from practice to performance.  They provide a musical application of the techniques we drill in our exercises. They also provide the opportunity to create and execute your personal interpretation of an entire musical work. 

Link from exercise drill to music making (e.g. Kopprasch)
Link to symphonic style (e.g. Blazhevich, Tyrrell)
Link to solo repertoire (e.g. Bozza, Boutry, Bitsch, DeFaye)
Link to versatility (e.g. Pederson, Gale, and other commercial/jazz etudes)
Link to trombone as holistic performing entity
Link to musical motivation

Etudes - a very brief overview

Kopprasch, 60 studies: Taking technique (agility, precision, execution) into music
(Similar: Bleger, 31 Studies, Arban Characteristic Studies, many others)

Rochut/Bordogni (by Rochut's own definition): “… to develop style in the interpretation of melody… development of sonorous, singing tone in all registers …”
(Similar: Bona, Concone, Lütgen, Marchesi, Vaccai, etc.)

Snedecor, Lyrical Etudes: the same as Rochut, w/more modern lines and harmonies

Blazhevich, Clef Studies: symphonic expressiveness and character study, clefs
(Similar, but without the clefs: Tyrrell, 40 Progressive Studies)

Uber, Symphonic Studies in Alto Clef: symphonic character studies, especially for 1st trombone in orchestral settings
(Similar, built on specific excerpts: Sauer, 20 Orchestral Etudes)

German Etudes: preparing orchestral, symphonic, and concerto styles

Bruns, Künstler-Etüden
Doms, Posaunenschule
Gaetke, School of Etudes (60 Studies)
Handrow, Neue Studien für Bassposaune
Müller, Studies and Concert Pieces

French Etudes: preparing advanced solo performance, expressiveness

Bitsch, 15 Rhythmical Studies
Boutry, Twelve Advanced Studies
Bozza, 13 Capriccio Studies
Defaye, Etudes

Marsteller: Advanced Slide technique (using Kreutzer, Popper, Czerny, etc.)

Maxted, Twenty studies: security and confidence in high register, symphonic

Tyrrell, Studies for the for Bb bass: low register (not just for Bass trombone!)

Raph, Diversified Trombone Etudes: overall maintenance, by specific techniques

Pederson (Kendor series), "Unaccompanied Solos": making technical study fun and musical (tonguing, flexility, etc.)

Pederson Etudes: commercial, studio styles - fun

J.J. Johnson, Exercises and Etudes for the Jazz Instrumentalist: Excellent new book, cultivates jazz syntax from beginner to advanced levels.

Jack Gale, 24 Jazz Etudes (w/ CD): idiomatic commercial, popular, and jazz styles