If you want to know what's the shortest connection from point A to B on a sphere (~ as our planet earth), which is likely the approximate route along which a plane will travel (so called "beeline" or "as the crow flies"), I can recommend the following tools:

1) Luftlinie.org
  • + Very simple to use: Enter text for origin and destination, confirm.
  • + Nice GUI:
  • Uses full available screen space
  • Shows linear/road/orthodromic lines next to each other for good visual comparison
  • Shows distance
  • + Results are saved as nice URLs, can easily be shared.

2) Google Maps Distance Calculator
  • - Handling is a bit harder.
  • - Layout lacks a little bit.
  • + Add arbitrary origin/destination point simply by clicking on the map.
  • + Allows multiple sequential beelines.
  • + Further features.

3) Related Wikipedia articles:

Great-circle distance in English.
Orthodrome, in German, but has better illustrations than the English article.