A small book of poetry, #1 in a printing of 400, by a relatively well known English poet who happens to be my uncle, and inscribed to "his niece of whom he is so proud, on the occasion of her graduation."
A copy of the complete works of Shakespeare that I won as a prize for acting in a high-school drama festival.
My "World of Pooh" that my parents gave me when I was four and has been one of my favourite books all my life.
A first-edition of Smith of Wooton Major that I bought for myself way back when it was actually on sale in a first edition.
A first-edition of Prince Caspian in dust jacket that my mum bought for me for about $15 but is probably worth the most of any book in my collection.
Some gardening books by the likes of Vita Sackville West and Marjory Fish that belonged to my aunt and came to me either directly or via my mother. My aunt has severe senile dementia and is as lost to me now as if she were dead, but I love her very much and love having things that she treasured.
And, oh my, so many. Probably those are the absolutely the most important, but, boy it would be hard to lose any of them.
Edit: I forgot to mention the hard-cover of McKillip's Harpist in the Wind given to me by the great love of my life when it first came out. There's nothing to show that he gave it to me - he didn't inscribe "with love" in it, or anything - but I remember when he gave it to me, and laughing over him having read it before me and teasing me by threatening to spoil the solution of all the riddles. Sigh.