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Why don't we give each other cash for Christmas? Your employer pays you cash instead of grocery carts full of stuff because you know what you want better than they do; why doesn't that go for gifts as well?
The usual answer is your Christmas gift is a signal, not just of your willingness to sacrifice cash for them, but also of how well you know them, to know what they want. But if so then why do we often make and distribute Christmas wish lists? Doesn't handing our free answer sheets defeat the purpose of testing them on how well they know us?
One answer might be that the gift receiver is like a teacher leaking answers to students to raise her teacher rating – maybe the gift receiver cares more that third parties think her gift givers know her well, than that they actually know her well. But in this case wouldn't she be trying to hide the fact that she passed around a wish list? If everyone who sees her get a gift was shown the wish list, who could she be fooling?
Could it all be an elaborate show so that she can honestly tell other folks that she got things she wanted? But if so wouldn't she be terribly embarrassed if they learned she gave out a wish list? That just doesn't ring true to me; what else could be going on?
Added: Registering for wedding gifts is a clearer puzzle; all are fully aware of the list, the list is very specific, and recipients don't save on shopping time/trouble, as they had to pick out the gifts.
Christmas Signaling
One of my relatives does consistently give cash (and only cash) to me and at least one other family member on Christmas, though we don't do the same in reverse. In my experience this works out well for all people involved.
Note that even when people give out a wish-list, it tends to be an actual list, and not just a single item that they want from each person. (I recall a South Park episode where Cartman requests a specific gift from each friend, in order to avoid the duplicate gift phenomenon, but of course this just reinforces Cartman's image as very crass.) I agree with jimrandomh's point that a gift retains an association with the giver in many cases, but I'd also want to stress that this is a two-way phenomenon. The recipient is more likely to think about the giver when using or seeing or thinking about the gift, but the giver is also more likely to think about her connection to the recipient on seeing the recipient using the gift. This feeling of connection is strengthened when the giver specifically chooses the gift. Presumably, the effect is strongest if the giver chose the gift from the universe of all possible gifts, but I suspect that it's still pretty strong even if there were only two permissible choices. If I were to choose between a stylish sweater and an iPod for a friend, then I would at least be reminded of my role in my friend's life each time I see her with either the sweater or iPod, and she would be reminded of my role in her life each time she uses one or the other. However, if she had just told me to buy the sweater, or told me to buy the iPod, this would deny me any agency in her life (at least with respect to this one salient choice), and (provided our relationship is a good one) thinking about my agency in her life is a benefit for both of us.