a good example of most modes is in church music, but a lot of world music is based on modes as well. you basically listen for the 'feel' of the piece - if it's centered in A, has a raised 3 and 6 and a lowered 7, that's A dorian. key's in G, but not the piece.
like they've said, the best example is the minor keys, but there's some other good examples in indian music with mixolydian modes, and phrygian modes in arabic stuff.