In part, it depends on what it was for, and on what’s stenciled on the crate. Something used for transporting a tripod won’t fetch as much as a crate once filled with grenades or mortar rounds.
I remember when the CMP would uncrate the cans of HXP they got, and throw all the wooden crates onto a pile that then got burned.
Last one I saw a couple months back at an estate sale was marked $10 and it appeared cleaner and less weathered looking than the one in your pic. IIRC, it was marked (2) 105mm How.
What prices are you seeing in Neb?
Seen a few for $30-50ish, and put up a WTB ad and got a bunch of hits with people asking what they're worth...which to me always translates to they hope it's a goldmine. I was thinking $10-15 range depending how clean.