I’m at a loss to come anywhere close to the rest of you. The best I can think of is Poe’s Complete Works, publ. 1927, which I bought about 30 years ago at a Berkeley flea market despite (not because of) its age. (I see the volume for sale at ebay for $25, so I guess it has a little antique value.)
Roman Empire coins are actually very common and not at all valuable for the most part. I have several in a cloth bag somewhere.
In the non-manufactured realm, I have a fossil-bearing rock that still has some of the nacre in it. We got it from a paleontologist researcher who told us that it is in the neighborhood of 62 million years old. 
A friend of mine had a human skull in her house. She claimed it was 4000 years old though I’m not sure if she’d had it carbon dated or if she just guessed.
Two old green Charles Dickens “Sketches By Boz” books, 1830 something. My grandfather left them to me - when I was young he caught me messing with them, and rather than scold me he offered to let us look at them together whenever I wanted to see them. I always told him that was probably why I became such an avid reader, and I was really touched when I found out he left them to me.
I have an 1854 US cent coin, That’s about it.
We have a first edition of “Life on the Mississippi,” 1883. It’s in crappy condition so not worth much. I also have my great-grandfather’s watch fob, undated but late nineteenth century. Trying to think what all else.
The house itself, is the oldest thing. It’s a drop-log cabin, built in the 1860s (which is impressive here, but obviously not so impressive in Europe for example!)
Probably my great-great-grandmother’s pestles. I’d have to look her up in the genealogy to give a circa, and I’d have to be home for that.
Forgot to mention in my OP: I also have a few ‘Daw’ books titled ‘Great Sf stories’ edited by Asimov, published in the early 1940s. Yellowing with age, the books may be antiquated, but the stories are timeless! Those books are worth buying; specifically check out # 5. Never did an anthology contain so many gems. Wow.
I don’t know I’m sure I have some old coins somewhere and probably other old crap I can’t remember off the top of my head, but the oldest really cool thing I own is the 1954 Sunbeam electric mixer I inherited from my parents – they got it for their wedding. It still works just fine, and fills the kitchen with that wonderful ozone smell every time I make whipped cream. Looks exactly like this: http://img0.etsystatic.com/014/0/7334196/il_570xN.432742026_qijv.jpg
In order of ancientness and only the oldest of each type:
I have a trilobite fossil – I have no recollection of how old it is if I was told.
I have several geodes which are ancient, I assume, though discovered and polished recently.
I have a Roman coin that dates BCE.
I have maps that date to the 1500s.
The oldest book I own dates to the late 1700s.
I have a grandfather’s clock that my grandfather owned that was made before 1911 when he got it.
Some paleolithic stone tools found by my father and me here and there in our region when I was a kid. Dad was in the state archeological society and worked on several digs. My family also roamed across plowed fields and firebreaks looking for artifacts.
As a small part of my metal working buisness I do some antique restoration, mostly old brass lamps. At home I have some beautiful oil lamps from the mid to late 1800’s. Other old odds and ends too, but I love those lamps.
At my shop we have some forging and hand tools that are over 100 years old that we use for the occasional odd task they were designed for. One I can date for certain from the serial numbers is an engine lathe I spent a few hours using today, is from 1906. The motor, a few bearings and a gear have been replaced over the decades, but I see no reason it won’t be working for the rest of my life. Thinking about it, of the 6 lathes we have, the newest is about 1950. Never really had this thought before, it’s all older than I am.
Sorry for the tangent; -I do love that reading this thread that as a collection of people we do love our old books.
I have “Grundzüge der Physik” (“Basics of physics”) from 1897. It’s from my family. Though it’s a detailed educational book aimed at students, it doesn’t provide any formula., which seems very strange to me.
A hymnal from 1786.
I have some Morgan dollars from the 1800s, a 100-ish year old rocking chair my aunt gave me, and a hope chest from my grandma that’s nearly that old.
They can all be derived, right?
I have my great-grandfathers (circa 1880) ceremonial Masonic sword. But the really interesting item is the fully renovated and operational Union Switch & Signal dual arm railroad semaphore signal along the railroad tracks to my rear. Always an eye-catcher for those driving by the property on the State Highway (36) just to the north.
Oops, forgot the date
Re: the semaphore signal. It was manufactured in 1912.
My house itself is over a hundred years old.
But for movable possessions, hmmm. I think it’s the candy dish from my grandmother, who got it as a thank you gift. It dates no later than 1923.