Hey I'm new, and I'm a trumpet player so I thought I'd toss some ideas in here.
The general range for the Bb trumpet is from E3 up to C6.
The lower register can be muddy if below Concert GHowever good trumpet players are able to play notes down to the concert E with ease and acceptable tone. I've seen unison low register notes used in pieces before with great effect. (See Tannhauser Overture-Richard Wagner). Notes to avoid:Low Concert B is very difficult to get down, this pitch is very sharp. Concert C isn't as bad, but younger players will still play it sharp as well
The Upper Register can be brilliant, beautiful, or harsh. Younger players will have considerable difficulty producing pitches above the concert F5 for a long period of time without rest. It is also very difficult to place these higher pitches perfectly in tune, sometimes to get within 5 cents is considered success. Avoid using high notes as a way to volume, while this is true they can be ugly and sometimes painful to the player depending on their ability in the upper register. Notes to avoid: Concert F is incredibly sharp for even advanced players, this is probably the most difficult note to place exactly in tune. Concert D will be very very flat for younger players. Concert G is also very sharp amoungst younger players. Even though notes above C6 are possible they should be used sparingly and not in soft passages or avoided all together in younger groups.
The Bb Trumpet plays very well in flat keys, and pretty well in some sharp keys. As more sharp notes are added, the more difficult it becomes to play fast passages, especially in the low register as the figurings become complex.
There are many types of trumpets the most common, the Bb trumpet and the C Trumpet. The C Trumpet plays in concert pitch and has a range simular to the Bb Trumpet, F#3 to D4.
Another instrument, the piccolo trumpet is common in orchestras and brass quintets. The range is very different than a regular trumpet though. The piccolo trumpet plays in either A or Bb and almost always has four valves. The range is from a B3(or Bb if in A) concert to an F6(E6) concert (G6 concert for talented players) Piccolo parts should be reserved for only advanced groups, such as college or professional ensembles. Anything below an Eb4 should be avoided as the tuning and tone below there is just ugly. The upper register is also very shrill and the most taxing areas of any trumpets range. The sound is very light and bright, unlike the larger horn. Most players will choose to play in A.
While trumpet do exist in other keys they are rare and with the exception of the Eb Soprano Cornet (used in British Brass Bands) are hardly used. For a band the trumpet parts should ALWAYS be written in Bb with no exception (a long time ago they were sometimes in A, but not so for the last several years).
In Orchestra the parts are sometimes in Bb but the standered norm is to write Orchestral Parts in C. In the past orchestra parts here written in E, F, Eb, A, D. But there isn't a need to do that, it only inconviences the player (although orchestral trumpeters are masters at transposition it's nice to not have to deal with it).
hope this helps somebody understand more about the trumpet, I Might do a simular posting on the Flugelhorn, which is simular but has its own unique details.