Air noise

Blowing through the instrument. Notated with a verbal instruction and perhaps rhythmic notation. Effective on the trombone and can be combined with slide motion or whistling. However, the single valve leaves little opportunity for simultaneous clacking.
Air noise:

Flap tongue

Flapping the tongue in the mouthpiece. Notated with x-noteheads and verbal instruction. Some pitches are avilable.
Flap tongue:

Multiphonics

Multiphonics are achieved by singing into the instrument while playing. Notate sung notes with small noteheads. Easy and effective on the trombone, although it is hard to sing a note lower in pitch than the one being played.
Multiphonics:


quartertones

Microtones

Intervals smaller than a semitone. Notations vary, but the examples above show a microtonal inflection and a quartertone. Microtones are easy on the trombone.
Microtones:

Removed parts

Removing sections of the instrument to play. Notated with a verbal instruction.
Removed parts:

Smacking sounds

Smacking part of the instrument with the hand. Notate with a verbal instruction. The most common is the mouthpiece smack, but smacking the instrument elsewhere (and various clicks and clacks) are also possible.
Smacking sounds: