Wow, I have so many favorites. How about three equally ranked favorites? These are all played on the Baritone Horn.
Gustav Holst's
First Suite in E♭for Military Band is one of the more fun pieces I'm played. It's bombastic, the Baritone part carries the melody for much of it, and it's a classic. My favorite movement is Chaconne, though the March movement is a close second.
You really need a full wind ensemble to pull it off, but
Inchon is an absolutely beautiful piece of music. My band made better helicopter noises than that recording, but you still get the idea. The melody is a combination of Baritone Horn and Clarinet, though in my band I got to play one section of it alone with a microphone to produce a brassier sound. That recording also slowed down waaaaayy more than we did in the middle slow section, but it's very emotional at any speed.
Coat of Arms by George Kenny is downright awful if you're not playing the Baritone Horn. By comparison, anyway. I literally play the melody in every single measure from start to finish. This piece is how I learned to play a high C without even blinking. This piece is how I learned to play low-low C without gasping for air. In the recording, take a listen at 2:00. Do you hear that high trumpet part? That's actually the Baritone Horn part. That lower part? Trombones. There were no trumpets back in the piece until 2:11. At first this piece was a terror. It has sixteenth notes, dotted eighth notes, triplets, a few measures of 5:8 time, and just about anything else you could possibly imagine thrown in. By the time we performed it in concert, I had it mastered. I taught everyone else the various melodies they played with me on occasion, and we rocked socks at the concert. It's the one and only time I have ever seen a band get a standing ovation in the middle of a set, and I am immensely proud of that day.