What’s your favorite classic trumpet concerto ?
Abblasen by Gottfried Reiche (if a fanfare counts, that is).
The Hummel concerto and the Haydn in E-flat are both very nice. Also, Telemann wrote a bunch of them; I haven’t heard them all (or even most…), but I tend to like his concertos.
Yes, I happen to have a recording of Haydn E-flat concerto and Hummel’s concerto performed by W. Marsalis. This recording is actually the reason for asking for more.
Brass music is a favorite, so the suggestion of Joe K is interesting - i hope i can find the recording.
I’ve got a special place in my heart for the Hummel concerto. I performed the first movement for a solo competition my senior year. I completely blew the high-range, large-interval jumping section towards the end, but I did fairly well for the rest of it.
The Canadian Brass has LOTS of trumpet concertos – Mozart, Beethoven, Tsiakovsky, you name it. 
If you’re looking for classical concerti, the most complete recording is Hakan Hardenberger’s 2-CD set. It’s not too expensive and I think it’s still in some stores.
For the Haydn, I recommend Maurice Andre or Gerard Schwarz.
For the Hummel, the above-mentioned Hardenberger recording is good. Rolf Smedvig’s recording is decent also. Armando Ghitalla was the first to record it; that’s considered the best by some. Edward Tarr has a ‘musicologically correct’ recording that I haven’t heard.
haardvark, there are no trumpet concertos by Beethoven or Tchaikovsky–by Mozart I assume you mean the composition of Leopold, the father of the more famous Wolfgang.
Zweistein, are you looking for trumpet solo music in general? Any trumpet music? I would just include every related CD I have but that would be around a hundrend and twenty.
IMO, stay away from Wynton’s classical recordings. They’re impeccably clean, but lack the independence or emotion that better soloists have. For classical concerti, check out Gerard Schwarz, Maurice Andre, Ole Edvard Antonsen, Sergei Nakariakov, or the Hardanberger I mentioned above.
A version.
You might have heard this on CBS Sunday Morning as the opening theme, although since 1998 they’ve used an all-too-clean version as played by Doc Severinsen on a piccolo trumpet. I prefer the version that sounds as if it was played on an eight-foot baroque trumpet.