The trumpet in all its various forms is a staple in many ensembles in almost every genre of music. In jazz the trumpet is one of the most historically important lead instruments and a crucial part of any jazz big-band ensemble. Trumpets are available in the additional keys of C and D but the Bb is by far the most common in contemporary and jazz music.
The most common trumpet used in jazz and contemporary music. The trumpet also comes in C and D constructions and while they do pop up from time to time the Bb is by far the most common variation.
The piccolo trumpet is also in Bb but tuned one octave higher than a standard trumpet. While rare it does pop its head up in jazz and contemporary music form time to time although it is usually not written for specifically.