As an alternative to isbndb (which seems like the perfect answer) I had the impression that you could pass an ISBN into an Amazon product URL to go straight to the Amazon page for the book. While this doesn't programmatically return the book title, it might have been a useful extra feature in case you wanted to link to Amazon user reviews from your database.
However, this link appears to shows that I was wrong. Actually what Amazon uses is the ASIN number and while this used to be the same as 10-digit ISBN numbers, those are no longer the only kind - ISBNs now have 13 digits (though there is a straight conversion from the old 10-digit type).
But more usefully, the same link does talk about the Amazon API which can convert from ISBN to ASIN and is likely to also let you look up titles and other information. It is primarily aimed at Amazon affiliates, but no doubt it could do the job if for some reason isbndb does not.
Edit: Tim Spalding above points out a few practical facts about ISBNs - I was slightly too pessimistic in assuming that ASINs would not correspond any more.