And why? Value may be construed in whatever terms you like (sentimental, monetary, scholarly, etc.).
I would have to declare a three-way tie for me:
1) A personally (and personalized) autographed copy of Walter Brueggemann’s Theology of the Old Testament: Testimony, Dispute, Advocacy (I have two additional personal and personalized autographed volumes by him as well).
2) A personally (and personalized) autographed copy of E. P. Sanders’ seminal Paul and Palestinian Judaism (I also have autographed copies of his two volumes on the historical Jesus; I had him sign these for me while I was at Duke; he retired my second year there).
3) An autographed copy of the novel The Oath by Holocaust survivor and Nobel Prize winner Elie Wiesel. This was a gift from a friend about 10 years ago, though I trust it is authentic.
Hopefully by the end of the year I will have a fourth book to add to this list, when my own, first book, is officially released with Eisenbrauns!
Hesed we 'emet 
Two way tie for me.
1) Deliverance of God — Douglas A. Campbell
I know this book has been generally rejected but for me it is extremely valueable (even if he is mostly wrong) for showing how much really goes into forming, defending and explaining a theological system. Plus, the sections that he has that forward his own view (vs. attacking the other view) are brilliant.
2.) Creation and the Persistence of Evil — Jon D. Levenson
I read this book about six years ago and it completely revolutionized everything I thought about the O.T. Since then the O.T. has been much more fun to read because I can now see the wonderful diversity and development in the views contained within it.
God’s Empowering Presence by Gordon Fee. Not only is it my favorite book and my first foray into academic writing on the Bible, I also got it personally (and personalized as you say) autographed while on a weekend retreat that he and his wife were at.
Ed Yamauchi gave me a good portion of his library which includes books given to him and signed by all sorts of scholars, I also have some of John Brinkman’s books, David Weisberg gave me an autographed copy of cuneiform texts that we read together in class, and my wife and dad have given me many books–each with wonderfully kind notes written in the front of them.
I have a personalized copy of Terence Fretheim’s God and World in the Old Testament.
Charles comment reminded me that I have a number of books my wife gave me for birthdays, Christmas, and Faher’s Day, and in each of them she wrote a sort of love note to me.
In fact while we were dating, not even 6 month in, I mentioned a book I wanted in an off hand way. One day she met me at the optometrist and while I was seeing the optometrist she went and put the book in the front seat with a love note in it. When I was leaving and and I went to my car I found the book and the note. It was the most thoughtful, sweet thing anyone had ever done for me. I treasure those books more than anything.
@Daniel: while I don’t own, nor have I read, Campbell’s volume, he is a former teacher of mine. I took a class on Romans at Duke with him; we never got past Rom 4, and I remember being unconvinced by his reading. But you are correct in the positive assessment of the HOW he addresses the arguments of others.
@Bryan: Very nice. Always good to have the ‘heroes of the faith’ sign something for you. I feel the same with Brueggemann, though I am fortunate now to consider him a colleague and friend who has encouraged me and my work in numerous ways.
@Charles: And which book from those is most ‘valuable’ to you? What scholars are included?
@Joseph: Very nice! Since Fretheim and I now know one another I am hoping to get him to sign the same volume you did, in addition to his The Suffering of God, which has been a formative and transformative volume for me.
Well, if our apartment was on fire and I could save only one book, it would be my NET-NA27 Diglot edition of the New Testament. It is not the most expensive book I have, but it has the most sentimental value to me considering that my wife got it for me. It was also the first scholarly type book I had and it was the one that stirred up a passion in me for academic biblical and religious studies.
Morphology / Morphologie: Ein Internationales Handbuch Zur Flexion Und Wortbildung/an International Handbook on Inflection and Word-Formation
One thousand pages of delicious linguistic science. $515 pages of research that I paid $14 for.
A first edition printing of the Expositor’s Greek Testament owned by an Anglican Bishop in the early 20th century.
A signed (& personalized) copy of Steve Runge’s Discourse Grammar of the Greek New Testament, which I had the great pleasure of working with Steve on.