I know that there are many ways to improve tone on the trombone, but I am running out of ideas. Could you post some of your favorite ways to improve tone?

Sorry, i accidently double clicked the button and it posted twice.

There are a million different ideas out there, some that work, some that are total b.s. And they are different from person to person. This is what worked for me.

There are two books I play out of regularly that work on tone, sound quality, and all that good stuff. They are:

"A Singing Appraoch to the Trombone" by Charles Vernon
and...
"Ben's Basics" by Ben van Dijk

Both books are amazing, each one changing my life and playing style when I got them. I noticed improvement almost right away, simply with the different concepts in each book. A Singing Approach is a bit cheaper, but it also does not have quite as much in it. But I would highly recommend either of those books.

And, of course, a private teacher always helps. They notice those little things we don't notice and can help fix little problems before they become huge issues later in life. (I sometimes wonder where I would be now if I had taken lessons in junior high and high school, instead of waiting till college.)

hopefully, this will not be considered BS
ok.. my take on tone production...
for a beautiful tone to happen
1... player must have a solid sound concept in his or her head.. if you don't know what you want to sound like, fughettaboutit.
2... player must be buzzing the correct pitch.. some players may chose to shoot low on the pitch to darken the sound. personally, i go for dead on.
3... the slide must be in the proper position to resonate at the pitch the player is buzzing. you will get the most overtones when the both are in line.
4....no extraneous tension.. yes the corners must be firm, tongue arched (more or less depending on pitch).. but cheeks, forehead, neck muscles, throat, legs, toes, etc must be relaxed.. practice in front of a mirror is very useful for diagnosing problems of this sort.
5....steady air
something to try
get out a tuner.. play an F# (in the staff).. don't worry about what the tuner reads yet, just play it. now, with your embouchure only, not the slide, start bending the pitch up and down slowly.. at some point, you will find a sweet spot where the horn just resonates and the note just seems to effortlessly jump out of the horn.. that point is where the slide is matched up with your buzz.. your pitch is centered. now look at the tuner, start making adjustments so you get that same feeling of ease but the note is in tune. now you have an in tune, well centered F#.
another idea
practice your long tones (you do do long tones, right?) with a drone pitch. intonation problems is a huge tone killer. find where the note comes out of your horn effortlessly and matches the drone pitch.. practice your lip slurs and arpeggios against a drone as well.. heck, why not your scales too, while you're at it.
i would venture to say that second only to tension, intonation (either buzzing the wrong pitch or having the slide in the wrong spot, or both) is usually the culprit to a bad tone.

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oh.. and a great book to check out
The Buddy Baker Tenor Trombone Method.. great daily routine, kind of along the lines of Remingtons, but more thorough, better instruction, and doesn't do all the same things every day. just a suggestion

Steve, totally agreed. Not b.s. at all.

You actually just hit evey point I make with my students.

A quick little something to add.... Do some work with just the mouthpiece. I avoided this for years, but when I finally started, I found that it really increased my tone quality and consistency in intonation.

Here's a little excersise I have my students play:

Start on F in the staff. Play a nice, full, long tone, then gliss down to the E nextdoor, playing again a nice full long tone. Now repeat with just the mouthpiece. Did you start on the same pitch? After the gliss, did you end on the same pitch? If not, repeat till you really nail the top and bottom note. Repeat from F to Eb, F to D, and on and on down to F to B. Now do it in different partials. That will really help you center your tone, zero in on intonation, and really find just where that match of lips, embouchure, air, slide, and, well, face, is so that you can find those "grooves" where the perfect notes live.

Another little trick i use, air is the key to good tone, so, just blow air through your instrument, take it right back to basics, blow air and think of the note you want to play, keep a full column of air...then buzz the note, then play it. I find that picks my tone up hugely in a simple, 20 second exercise.