At the Fletchers' last weekend, I talked a bit about dreams with John after he heard I was taking the Lucid Dreaming class. I mentioned at one point that I knew someone who had told me of a prophetic dream she once had. The details of the dream are uninteresting (her car was in the shop and she dreamt correctly of the part that was broken and the price to replace it, before finding it out the next day). The fact that it happened at all was fascinating. But John seemed to find the idea worrying as well, saying that if such things were true then it would have tremendous implications for the (non-)existence of free will.
To me, though, that doesn't seem to be a problem. Rabbi David J. Wolpe (in his book Why Be Jewish?) said that "Prophets do not foretell the future; rather, they see deeply into the present." I'd say that's the approach I take to thinking about this kind of thing.
Let's say I tell you what I'm going to do for the rest of the evening. I'm going to finish this blog entry, call my sister on the phone, and later on watch Whose Line is it Anyway? while I work out. This information will probably be a bit outdated by the time you read this, but you can see the concept. This is the present giving you very clear information about the future. It's not perfect, of course. I could get hit by a meteor, which would cancel the whole thing, or I could simply decide to read instead of watching TV. But it would be perfectly reasonable to trust me and assume that in all likelihood things would happen more or less as I described. And nobody's free will is affected by this at all.
So I believe this is the kind of knowledge that people get when they have prophetic dreams, or when they obtain information about the future in other ways. It isn't perfect or exact, and it doesn't plunge us all into determinism. But it could still provide enough information to be useful and/or interesting. Of course, it would raise lots of other questions as well. If you find that some of your dreams are predictive, you'd have to learn how to tell them apart from the ones that aren't. Notice also that I'm leaving aside the whole question of where this knowledge even comes from, simply because I have no clue. I think it would have a lot more to do with "seeing deeply," as Wolpe says, than with simply being told things, but there are probably lots of little mysteries inside us that would affect things like this.