My oldest is this Greek Tomis, 200-100 BC. Hermes head right (cool hat eh?), Caduceus with wings, TOMEI AOAE (Moushmov 1772, plate III, 30 - thanks to a sharp-eyed collector for help with that attribution).

My oldest "standard" numerical dated coin is this German (Hanau-Munzenberg) 1614, 3 kreuzer.

My oldest US coin is this, barely identifiable, 1798 large cent that I am very proud to have in my collection.

Finally, an honorable mention to this double-struck
Constantine I Licinius follis as my oldest error (@310 AD).

Every time I get involved in one of these "your oldest..." threads, I start thinking about trying to put together a one per century set.