My sister has my grandmother’s Lithuanian prayer book, dated probably 1880s, which came over from the old country. Oldest book that has been in my family.
My partner has a History of Duelling from MDCCLXX 
Two Marriages, 1867.
An 1856 edition of Longfellow’s “The Builders”. Gilt edges, full color pages, small but very pretty. Given to my mother by her great aunt Flo, and I got it after mom died. The cover isn’t in great shape (I think it spent most of its existence in mom’s sock drawer) but the interior is still very beautiful.
My mother has the New Testament she was given when the Queen was coronated. Not that old, but pretty special. Her brother bit and chewed the corner of it(he was a teenage, but a mental case…uh, jerk).
My Father found a family Bible with births and deaths when his own mother died in 2006. It was from the late 1800’s. Helped with our family tree, too.
His Father had a German Bible from when he was a teenager in Germany in the 1920’s. Very nice.
Bibles tend to stay around if they are nice. Shame everyone goes “Bible App” today. They are kind of cool.
Most of my books are catalogued on LibraryThing. According to their data, an edition of Gulliver’s Travels from 1881 is the oldest book I own that has a known printing date. When I was about ten, I found it in my father’s old room in my grandmother’s house and he let me keep it. There were a bunch of other books I got the same way but most of them are now lost.
I also have my great-grandmother’s family Bible which is probably printed about 1885-1890.
It’s OK, we know. You can admit that you ate them.
I’ve got a bible that was printed in 1611. It’s not a first edition King James, but probably the last edition of the previous so called “Breeches Bible.” It’s in pretty bad shape. It’s belonged to my family since the mid 1800’s.
A first edition of Jurgen, by James Branch Cabell. Bought it on a whim when I saw it priced cheaply at a used bookstore in San Antonio.
I’ve got a copy of an anonymous book published in 1852 called The Mormons: or, Latter-Day Saints, a contemporary history, with memoirs of the life and death of Joseph Smith, the “American Mahomet.”. Somebody – almost certainly a librarian – wrote some annotations in pencil on the title page, indicating that the author was Charles Mackay, the author of the much more popular Extraordinary Popular Delusions and the Madness of Crowds. On the back of the title page, the librarian proved their SDMB-worthiness by writing in a citation which says:
I’m pretty sure that’s the oldest book I have, assuming we’re going by “when this physical book was printed” and not, you know, when the content was written.
I have a 1909 1st edition copy of Girl of the Limberlost signed by the author. My great-grandfather was a professional photographer and met author Porter in the course of his work. She provided the book, signed to his four daughters.
H. Rider Haggard collection - matched binding - from 1890’s
I have a 1631 edition of Thomas Beard’s Theatre of God’s Judgments. He was Cromwell’s tutor and the book consists of chapter upon chapter of the ghastly deaths of murderers, tyrants, fornicators, atheists, blasphemers, etc. It’s a fun read!
I just got Volume 1 of An Account of the East Indies by Alexander Hamilton (no, a different one) published in 1744. The binding is in very poor shape; I’m trying to find out how to repair it myself. The book was cheap and I have no particular attachment to it, but I’d like to see it make it another 270+ years.
The Sinking of The Titanic and Great Sea Disasters from just after the sinking, probably 1912-13.
Crass attempt to cash in on the notoriety. It’s pretty damn cool, though.
I have a first of edition of Louisa May Alcott’s Jo’s Boys, which was published in 1871, I believe.
My English professor at the University of Michigan owned a first edition copy of Tristram Shandy, which was split into smaller coat-pocket size volumes. From the 1760’s.
2-3 of the volumes…were signed by Laurence Sterne as a form of copyright protection.
He died in 1768 and I held books written by him. We flipped through the pages and everything. It was incredible.
Probably the oldest museum-type item I’ve touched.
I have a single page from a First Folio. It’s from Measure for Measure. My father acquired it somewhere. He traveled a lot in his 20s.
Aside from that, I have a number of books from before the US Civil War-- maybe 7 or 8. My grandfather collected oddities, and his collection got passed down to the grandchildren. I got a lot of the books, including the oldest ones, plus all his True Crime books, of which he had a lot, because he was a crime reporter. He even held the position of editor for a number of years. Wichita Eagle.
Yeah, very cool.
I collected first editions for years. I sold my 1784 Shakespeare - it was the first Octavo single volume (in the forward, it was praised as a volume the common man could afford or that a gentleman could keep in his coach to win bets on quotes;))
I have a few earlier books that my dad had acquired, but none stand out.
From a coolness factor standpoint, I still have a first of I, Robot (sold my Foundation Trilogy) and I have a Review Copy of The Autobiography of Malcolm X sent in advance to Congressman James Roosevelt, FDR’s son. And a signed hardcopy Snow Crash and the limited first hardcover of Watchmen. Oh, and the Aerosmith bio Walk This Way signed by the band. Stuff like that 
1898 leather-bound collection of Kipling. Terrible shape, alas: the leather is peeling away from the old newspapers (!) that made up the pastboard for the covers.
(Amusing that the spines have swastikas as decorations. Long before those brown-shirted boobs highjacked the image!)