I'm writing a proposal for a book and have been asked to provide examples of similar books and list how my own work is different from them. Unfortunately I don't know how to approach this question because there are possibly many other books that share similar themes/plots/characters/etc that I've never read. How can I go about searching for books that may share such characteristics with mine (or any others I wish to write in the future)?
The point of this is to help the person judging the proposal know how to position and sell your book. If there are other books in the same general space, it shows that there is a pre-existing market. This may be harder to demonstrate for a book that is well and truly unique --unfortunately in today's marketplace, no one wants to be a pioneer. On the other hand, however, even the most experimental book typically has "distant cousins" it may resemble. The thing to remember is that ultimately the question isn't really what books are like yours?, it's what audience will buy your book? A book quite different from yours could be a good comparison if it has the same audience.
The only way to do this well is research --at a library, bookstore or on the internet. A mistake I've personally made in the past is to use too many bestsellers as comparisons. While it might seem that this would position your book as a future hit, it actually makes it seem like you only know the "greatest hits" among your competitors.
Once you've established that yes, people do in fact buy books like yours, the task shifts to showing why the world needs another entry in that category (in other words, what makes your book special).
Unlike Chris Sunami, I suspect that this task was not given to help the agent or publisher better sell the book. They are professionals and (should) know their field. If they don't, you have chosen the wrong publisher.
I rather believe that these professionals want to see if their prospective new author is a professional, too, and knows the context in which he is writing – or if he is ignorant of the literary tradition and artistic context in which he stands and with which his work is in dialogue with. After all, authors of a certain level of literacy are expected to write (give interviews and theorize) in relation to what goes on around him, and not write from and for himself.