Hey, cool! It is rather waltzlike, isn’t it? 
A couple more –
The Non nobis sequence from Branagh’s Henry V (score by Patrick Doyle) as the camera pans over the battlefield. That gets me every time, and I’ve seen this movie how many times now? 
And one from Fellowship of the Ring (score by Howard Shore):
The slow, ethereal choir and the soprano solo after Gandalf’s fall in Moria. Beautiful.
This isn’t exactly background music, but I love the scene in Amadeus where Constanza brings a stack of Wolfgang’s “scribblings” to Salieri to find out if they are any good.
The music switches from piece to piece as he flips through the stack, each one more magnificent than the last. It really conveys Salieri’s frustration: He can hear them perfectly in his head, but he knows he’ll never produce anything like them.
There are different pieces of music from Trek that I feel made the show “be there” for me. The fanfare used in some of the first season episode title scenes (just as the show starts, the title of the episode is onscreen), like in Balance of Terror and What are Little Girls Made Of?, gives me chills. The mysterious effect music, used first in the second pilot- listen to the scene where the Enterprise is approaching the energy barrier at the edge of the galaxy. The flute(?) piece played when something alien is being introduced, like the scene where Clint Howard offers Kirk the alien drink Tranya in The Corbomite Maneuver.
(It’s funny, Tranya tastes just like a screwdriver, maybe with a little passion fruit. Go to the Las Vegas Hilton and try it yourself.)
On a slightly different note: I also liked the theme music used in the first two or three episodes, where there is no “Space, the final frontier” voiceover and the music is more “spacey”- it’s the only word that comes to mind. It doesn’t have the funky 60’s percussion found in the 2nd and 3rd season eps, and it sounds like a synthesizer, not the classical instruments used for the rest of the season.