Richard Strauss famously quipped "Don't look at the trombones; it only encourages them." It is an ironic observation coming from a composer/conductor who wrote really well for the trombones.
Trombones are the soul of the brass ensemble - capable of tremendous power, dolce lyricism, and quiet elegance. The technical potential of the trombone is often misunderstood, as is its ability to beautifully execute a melodic line in any register of the instrument.
The fact that most orchestral scores use three trombones originates from its use in the church, where the family of trombones was used to support choral lines; the alto, tenor, and bass trombone choir was carried over into orchestral music. Used famously (but sparingly) by Mozart and contemporaries, by the early 19th century the 'best practice' of three trombones in an orchestral section was firmly established. It wasn't until the late 19th century that composers started to move away from using the alto trombone, even though some composers (particularly in Russia) continued to write alto clef parts well into the 20th century.
Trombones are very effective in just about any role you assign to them. When I first enter notes in a brass ensemble score template (see Getting Started), I will enter the tenor line from the keyboard score into trombone 2. This makes moving the tenor voice into trombone 1, euphonium, bass trombone, or either horn part a conscious decision, and keeps me from just dumping tenor lines into trombone 1.
Many composers write a 3 or 4 voice homophonic texture in the left hand which suggests trombones first, though I diligently look for ways to vary that practice; flugelhorn, and 2 horns is a lighter texture; flugelhorn, horn and trombone is a slightly heftier sound; 2 horns and euphonium is darker and more subdued - there are many possible alternatives to just putting the 3-voice tenor register chord into the trombones.
I am always on the lookout for a mezzo, alto, or tenor melodic line that works idiomatically for the tenor trombone. Bass trombonists are people too - always look for opportunities to write melodically for the bass trombone.
Range, technique, chord voicing ... all subjects for a future entry.