Let me quote what Le_Tromboniste wrote in the viola forum:

By the way, viola isn't the only instrument to use the alto clef. Trombone also does.

Yes, I saw the alto clef for the alt trombone in a number of orchestral scores. Yet, I have two orchestration books which claim that the alto clef is no longer in use since the use of the alt trombone is limited.

I would like to hear the opinion of trombone players on this matter. Myself, I wonder if the potential saving of a single ledger line at high pitch notes justifies the use of the alto clef. The question is, of course, what clefs, nowaday, is the the trombone player obliged to be familiar with.

You MUST know BASS and TENOR CLEF. If you plan on playing any first parts you have to read Alto Clef. And if you plan on playing anywhere outside the United States you need to know Treble clef as many "world parts" are in treble clef.

Thats what I said. First trombone part in most editions of most orchestral repertoire (at least up to the late 19th century) is written in alto clef.

As for your books saying the alto clef is not used anymore, they're, as you said, orchestration books - meant to be used mainly by composers and arrangers. Composers don't use the alto clef for trombone anymore, true. However trombonists still have to read it since most of our orchestral repertoire dates back to when alto clef was common.

You also mentionned the alto clef being meant for the alto trombone (thus its decline, since the alto isn't used anymore).
This is a wide-spread belief, but probably an erroneous statement. Many orchestral parts do show ''Alto trombone'' in the top left corner (which leads many trombonists to use the alto to play them), however these are all recent editions. Try to find a manuscript that does. You won't find many, and this is because alto trombone probably never saw wide-spread use (it's actually used more nowadays than it ever was before). I won't go into details here, but extensive research was done on that matter by a few specialits (thinking of Howard Weiner, most notably), and leads to think that the use of the alto trombone has always been very limited. Most of the repertoire is easily playable on a tenor (plus, tenors in the past were smaller in bore and bell size, meaning they were easier to play in the high register) and often partly unplayable on the alto (period alto, that is - in-tune 7th position on the alto didn't exist until very recently). Plus, the blend is better with tenors. Anyway, I'm way out of topic here. Read Weiner for in-depth explanation if you want to know more.

More information about clef use - I don't know what books are being referred to above, but a review of my 'Orchestration' books indicate Alto Clef is used for writing in the 11th and 12th harmonic partials. If you are going to paly in a section Alto cle fis used for both 1st and 2nd tenor trombones commonly. Debussy writes in Alto clef for all three trombones at times.

Some modern Russian composers still use the Alto clef.

Here's my take on clefs:
You should learn as many as you can. If you are trying to avoid learning one you should rethink what you want to do with music or what instrument you want to play. If you have any desire to perform even in a top quality community orchestra you need these clefs. Also when you know your clefs you can use clefs to help transpose when you need to. I was taught Treble, Bass, Baritone,Tenor, Alto, Mezzo-Soprano, and Soprano clefs. There is also a clef called French Violin Treble clef, you would be surprised how often I get to employ this clef.

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Steve (just below this post) says it very well.

It all really depends on what you want to do.
If you just want to play in a wind ensemble, church or community band, bass and tenor should suffice.
If you want to play in an orchestra, especially principal chair, you'd better be fluent reading alto as well. It wouldn't hurt to be fluent reading concert treble either.
If you want to play commercial music, concert treble reading is a must.
If you want to teach music, conduct, or compose, be able to read all of the above, and know the transpositions.
As for the other moveable C clefs, I haven't come across the need for them enough to devote the time them, but if they serve you well, have at them.

the note trainer in the tests and games link below is a great way to learn and be proficient in bass tenor alto and treble clef

Thank you, all, very much. I greatly appreciate your feedback.