This is from a bibliophile's perspective. I make no claims about content or emotional attachment (well, none until the end anyway.)
A perfect book to a book collector is a hardcover first edition and a first printing (collectively known as a true first.) The dust jacket is intact with no scuffs, tears, or wear of any kind. There are no dog-eared/missing/marked pages. There are no black remainder marks on the book's body, and the dust jacket hasn't been punched. Water damage is a dealbreaker - the book should close normally with the two covers parallel to each other and, when smelled, there should be no trace of mold.
Ideally (and we're talking strictly about ideals here, anyway) it will be autographed.
Some first editions (particularly of big big big name authors) are of an extremely limited run and are leatherbound or with special bindings of some form.
On a personal level, an important factor to this whole enterprise is finding a book that has been read and cared for extremely well. New books are fine, but...if it feels like you're holding something cherished by someone else if your hands, the sense of personal history encased in those pages is almost worth a little damage. I like my bindings broken in (not cracked - there's a difference) and I don't mind fingerprints on the pages. I like my books to come with a history of their own.
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