You can download PGN game databases of specific players on pgnmentor.com and browse that way. Only way I know to do what you're talking about is using Chessbase or maybe SCID
Is there an opening database for specific prominent players?
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At chessgames, there are pages like this for many players.
http://www.chessgames.com/player/viswanathan_anand.html
Last night I was looking up openings for Paul Morphy and Kasparov. I saw a few websites that just mentioned what openings they played the most but the only move by move database I checked out was on chesstempo. However, I did not see a white or black option which made me wonder if the responses and the moves were made my Morphy or by the opponent in those positions.