It has recently been said to me that the Hebrew phrase for "A Psalm to David", which appears at the beginning of many Psalms, should actually be translated "A Psalm to David".
The Hebrew text for "A Psalm of David" is, לְדָוִד מִזְמֹור. The person said that the lamed (לְ) in front of David's name (דָוִד) indicates that the phrase means "To David", and not "Of David"; in other words, the phrase is not indicating that the Psalm was written by David (though whether or not it actually was written by David is irrelevant to the discussion; I believe that the relevant Psalms were, and I believe that that person believes so as well), but are speaking to David.
In other words, if לְדָוִד מִזְמֹור means "To David, a Psalm", then one could say that, although David was the author, he was not the speaker, but was writing to himself from the perspective of someone else. If לְדָוִד מִזְמֹור means "Of David, a Psalm", then there is no good reason to deny that David himself is the one speaking. Consider the importance of this when interpreting Psalm 110, for example.
Is there any good reason to say that the lamed in front of the Hebrew for David does not mean "to", but rather "of", or that it indicates possession? I myself can say that certain of those passages which begin with לְדָוִד מִזְמֹור don't seem to address David at all, but instead seem to be written from his perspective.