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I was trying to think of examples where composers used the same music in two different pieces (but not including transcriptions they made of one of their pieces). I could only think of a few examples:
Rachmaninov used the opening of his Romance for 6 hands in his Piano Concerto No.2.

Schubert used a theme from an earlier sonata in A major as the theme for the Rondo of his Sonata D959.

Beethoven used a motive from his Eroica Synphony for his Eroica Variations Op. 35.

My guess is there are many more examples like this. Can you add to the list?

Schubert "Trout" is the first thing that comes to mind for me...

That reminded me of Schubert's Wanderer Fantasy and song of the same title.

It also kind of depends on how strict you are on “same” music. Mozart for example like to use that “Mozart’s in the closet” motive, or similar. And one of the themes from the piano concerto 21 that sounds like a theme from one of his horn concertos etc.

Chopin Nocturne op 20 and second piano concerto third movement

The Baroque composers were all very thrifty, and recycled their own music all the time, as well as recycling other composers' music for their own devious, er, I mean, environmentally-friendly ends.

Viv's quadruple violin concerto turned into Bach's Quadruple Keyboard Concerto. Alessandro Marcello's Oboe Concerto turned into Bach's keyboard work. And so on.

Handel was a master at recycling. For example, in Messiah, "Unto us a child is born" and "All we like sheep" came from Nò, di voi non-vo' fidarmi; and Se tu non-lasci amore from 1722 became the basis of "O Death, where is thy sting?"; "His yoke is easy" and "And he shall purify" were drawn from Quel fior che alla'ride. And his famous aria Lascia ch'io pianga had two previous incarnations - first as a sarabande from Almira, then as an aria in Il trionfo del Tempo e della Verità before its most well-known form in Rinaldo:

https://www.youtube.com/watch?v=EKo_EmfEPWs

And not a lot of people know that Beethoven's Op.49/2 Minuet was re-used in his Septet's Minuet.

Schumann re-used a theme from Papillons in Carnaval.

Lots, lots more......

Also, you didn’t specify whether or not the musical material is necessarily original. If not, then you have for example Rachmaninoff using dies irae in several settings.

Bach's Cantata #156 chorale made it into the slow movements of 2 concertos: BWV1056 in Fm for keyboard and BWV1059 in Dm (oboe solo). Various arrangements of the piece under the title "Arioso".

Some of the hymns in a Bach's oratorio get recycled in another in different keys.

Good examples. The Beethoven and the Schubert came to mind for me right away, and I didn't think of any others.
I didn't know about the Rachmaninoff.

BTW, Beethoven also used that theme in the Prometheus ballet -- and actually (I didn't know this before -- only saw it just now when I went to check) the Prometheus came before both the Variations and the Symphony.

Beethoven's Op. 2 No. 3 (1st mvt) and Op. 2 No. 1 (2nd mvt) use material from his earlier Piano Quartet, WoO 36 No. 3. And that Eroica theme appears yet again as No. 7 of the 12 Contredanses, WoO 14. Beethoven really loved that tune.

The last movement of Mozart's Concerto #27 uses the melody from his song "Komm, Lieber Mai."

A melody from Beethoven's Gegenliebe is used prominently in the Choral Fantasy. And I just discovered that a different section of the Prometheus finale was refashioned as No. 11 of the 12 Contredanses.

Bach reused many of his themes from one piece into another. For example the opening of cantata 29 which is also used in the violon partita 3 prelude. He borrowed quite a few pieces from other composers as well.

Thanks. That explains my confusion on seeing Rachmaninov's transcription listed as a transcription from the violin partita and some other transcriber saying it was a transcription from the cantata.

Schumann's Ghost Variations theme is taken from his violin concerto, although he didn't recognise it owing to the deterioration of his mental faculties.

Mitsuko Uchida has suggested that the Arietta from Beethoven's Op.111 may have started out as one of his Diabelli Variations before taking on a life of its own. I can hear the similarity.

Also the amazing Gratias Agimus Tibi from the B minor mass is from an early cantata, but I forgot which.

I know this is not what you're looking for, since it's a rearrangement of an own existing work, but Liszt's famous "Liebestraum Nr. 3" is a solo reworking of the song "O lieb, solang du lieben kannst". A very moving text:
O love, o love, as long as you can love
O love, o love, as long as you may love
The hour will come,
When you will stand by graves and mourn.

Full translation here.

I love this recording- Cyrille Dubois and Tristan Raës are fantastic musicians:


An example from the orchestral repertoire: Mahler's song "St Anthony's sermon to the fish" later became the scherzo of his 2nd symphony:


(poor quality recording, but chose it for the subtitles).

Mahler certainly re-used many themes from earlier songs (from Das Knaben Wunderhorn) in his symphonies.

The finale of his 4th (a child's vision of heaven) is a song that he originally wrote seven years earlier, for instance: in fact, the whole symphony is built around that song Das himmlische Leben.