Several other people have been discussing their oldest books. Since I've not biblioblogged in a while, I'll mention my oldest.
My penultimate is Polybius, ex recognitione, Immanuelis Bekkeri, printed in Berlin in 1844. It was originally a two volume set (owned by Paul Geyer in 1867, and one Benedict Einarson some unspecified later time). At some point both volumes were jammed into a single library binding. This was a very high quality production, the binding and paper are sound and usable to this day, with minimal foxing.
My oldest book is ἩΡΟΔΟΤΟΥ ἹΣΤΟΡΙΩΝ ΛΟΓΟΙ Θ’, textus Johannis Schweighaeuseri, Volumen Secundum printed in 1818, apparently in Glasgow (Glasguae?). The paper is in good shape, though it has a lot more foxing, but the cover is falling apart. Once in the library of the Kimball Union Academy, Shelf D, No. 75, (which institution still exists).
I probably have a dozen more books from the late 1800s, mostly Greek topics. While I love a good, old book, I expect all of my books to survive actual use. For editions of Greek texts, I'm usually a more eager collector of the most current edition available, because I love a giant app.crit. more than I love the aroma of old books.