Hello, Hear are a few more to add to Peter Goldstein's interesting list.
Firstly, popular borrowings:-

(1) The 1930's English popular song, "Yes we have no Bananas", opens with
the same 4 note phrase as Handel's Hallelujah Chorus.

(2) The opening of one of Prokofeiv's violin sonatas bears a striking
resemblance to the 1890's English music hall song, "If you want to know
the time, ask a Policeman"

(3) Another music hall song of that period,Two Lovely Black Eyes", Sounds
as if it had been derived from the scherzo of Spohr's 5th symphony.  Now
some more serious possible borrowings:-

(4) Still on the subject of Spohr's 5th symphony.  In this work, written
1837, Spohr seems to have copied the idea of a motto theme from Berlioz's
Symphonie Fantastique, which appeared 7 years earlier.

(5) The finales of Haydn's Symphony No 13 in D and Mozart's Symphony No 41
in C both share the same 4 note phrase which, in each case, is treated
contrapuntally.

(6) The opening theme of Beethoven's Eroica Symphony seems to have been
lifted from one of Carl Friedrich Abel's symphonies (was it Op9, No 6?)
Beethoven didn't hesitate to recycle his own themes when it suited him; as
in case of the main tune in the finale of the same symphony, which is well
known to have been lifted from his earlier Prometheus ballet music and was
also used for a set of piano variations.Similarly, he took the minuet tune
for his Septet from the rondo of the early piano sonata which his brother
got hold of and published as Op 49, No 2

(7) Mahler's First Symphony bears striking resemblances, certainly in style
if not in thematic content, to his friend Hans Rott's E major Symphony,
Completed 8 years earlier.  Sadly, Rott died in 1884 in his mid 20s.

(8) The English composer, Sir Hubert Parry (1848-1918) Seems to have
borrowed the scherzo theme of his 3rd symphony from the finale of Raff's
6th symphony and the opening of his 4th symphony bears a striking
resemblance to that of Brahms's 3rd symphony.

Of course, some of the above examples might have just been
coincidences---"Great minds think alike." Nethertheless, I think that
thematic and stylistic resemblances make a fascinating study.

Cheers,
John H. White
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