For trombone playing, I play on a Greg Black/Joe Alessi 5.5 Medium weight. (I am considering switching to the 3.5). I have played nearly every trombone mouthpiece made, and these mouthpieces just get the best results. They cost a good deal more than most mouthpieces running in the area of $145 each, but it's really worth it for what you get out of them.
Generally, I like for the line to play the same mouthpiece for intonation, and tone matching reasons, but if someone feels uncomfortable on something, and/or plays a mouthpiece that works well with what we are doing on the field that doesnt bother me. For instance, we have a euphonium player who plays bass trombone in the off season and sounded great with his Bach 1 1/2G so I let him play on that in the line.
At Court of Honor, most of the line are on the following mouthpieces:
Trumpets: UMI 3C CKB
Mellophones: UMI 6V
Baritones: UMI 4G
Euphoniums: Bach Megatone 3G (custom)
Tubas: UMI Helleberg