I have my grandmother's Atwater Kent Radio.  I also have a Tommy Ticker watch given to me by the ancient Mr. McCann when I was a very small boy.  I'm not really sure which is older.
     I also still have my first new two wheeler, a fire engine red 1960 Rollfast 26" bike.  It's in need of a little TLC but it could be made functional again for little expense.  Bikes were made of solid steel back then.
     And of course there's me.  I'm pretty damned old.

Rocks! They're pretty darn old. I guess it's sort of cheating, though, as they aren't manmade, and are all around outside.

The oldest manmade things I have would probably be photos and possessions from ancestors and relatives. This includes some type of old camera. I forget what type it is, but apparently it's pretty common. There are also a few old bibles, one of which has a long-since-passed relative's hair in it. I think they're from sometime in the first half of the 20th century or so.
I've also seen some tobacco and a carved pipe from a relative who was in the American Civil War, although that belongs to another family member.

I have a Civil Engineer's handbook from 1919.

A hewing hatchet from the early part of the last century. Although these days my back feels even older. 

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I do own a couple of Roman era lead glandes. After that, my grandfather's gold pocket watch from the late 1800's. i only wear it for special occasions. If I ever break it, he will come back to haunt me.