Fly Me to the Moon
Big band. This has a very jazzy feel to it. Note how MIDI volume and MOD controllers are used to add realism to the horn parts.
New York, New York
Big band. Although not written in the 40's, it could have been.
In the Mood
Big band. One of the most famous "jitterbug" tunes, recorded by Glenn Miller. It's actually a simple blues progression. (Interestingly, when the composer first presented this tune to Glenn Miller, he rejected it as not being "hip enough". Popular tunes of late 30's were a bit more substantial melodically and harmonically than a simple blues progression. After a few years of prodding, the composer finally convinced Miller to give it a go in 1941, and it became one of Miller's most popular numbers. Geez, I'm starting to sound like that guy on "Arts and Entertainment" TV).
I Left my Heart in San Francisco
Bass, drums, piano, vibes. A slow ballad made famous by that MTV guy, Tony Bennett. This arrangement has the introductory "verse" (before the "I left my heart..." comes in), which a lot of musicians think is nicer than the chorus which everyone knows. (Here on "A and E").
When the Saints Come Marching In
New orleans "jazz". Essentially, everyone just solos at once, in order to make as much chaotic, uptempo noise as possible.
A lot of Big Band and "stage band" (or "jazz band") arrangements can be found on Gary Wachtel's site. You can access this via Gary's Web Page.