I did a reading (a CC to be exact) back when I started learning the tarot, which I had nearly completely understood, except for one card -- the Ace of Swords. I believe it was in the 8th position, which in the variant of the CC I use, represented others' view of the situation at hand. I can't remember exactly what the question was, or any of the other cards, but I do remember that much.
The Ace made no sense to me until a thought occurred to me, and I manually turned it around, so that it was reversed. One blink, and everything fit together. I've used reversals ever since.
For me, reversed cards can have entirely different meanings (especially when some cards look very different reversed than upright), or simply help to indicate their position or purpose within a spread. I don't have any particular way of reading them, but they do seem to serve a purpose every time I see one. For me, it would be much harder to read without them than with -- but I always have been a tad different.