Sousa, Semper Fidelis or The Stars and Stripes Forever ( both great; I can’t choose between them ).
Joplin, The Maple Leaf Rag.
Chopin, Nocturne Opus 9 #2 or Fantasie Impromptu in C sharp Minor Opus 66 ( both are great!).
Any Mozart clarinet or flute concerto; sheer loveliness.
Beethoven Symphony #5.
Beethoven string quartet #16 in F major Opus 135 ( his last work before he died, and very unusual Beethoven ).
Bach Brandenburg concerto #5 ( #2, and #3 are great also ).
Bach keyboard concerto in D Minor; here’s an amazing performance of this great music by 9 year old virtuoso Alice Burla: http://www.youtube.com/watch?v=fwvWrKdXDVc
Mendelssohn Violin Concerto, or if you prefer, A Midsummer Night’s Dream.
Tchaikovsky, The Nutcracker.
It’s hard not to pick a hundred more pieces of music...
In particular Beethoven's string quartet opus 131, from Pharmboy's list. I wrote a college paper on it. The piece was arguably an early peek at 20th century music.