Flow and story is a little more important for concept albums, I'd say. For regular albums, song order should be structured so that things avoid blending together too much and not sound like they're in blocs by structure or sound. This is probably the most important make or break factor of enjoying an album straight through.
As an example, I'll say Sabaton's Art of War. For power metal, all the tracks are great on their own, but the album as a whole becomes tedious and drawn out because of the order of the later half.

I listen to albums as a whole, but I like each song to be its own story; there can be an overarching feeling or narrative, that may evolve, or not, but the majority of songs should be able to stand up on their own. I don't like to feel as though I have to commit to an hours worth of music in order to be able to appreciate any one piece fully, though as I said, I listen to albums in a sitting once I know that each song stands up in its own right.