A lot of new furniture is veneer over particle board, and that may be what some think of when they hear "veneer". Most of you expensive antique furniture is veneer - and it's a nice thickness and beautiful. Nothing like a nice bookmatched set on a table top.
Newer veneer can be paper thin, and real easy to sand right through if you don't know what you are doing. I've seen so many old furniture that someone tried to "refinish" with a cheap power sander and 80 grit paper.
Last time we were in the Twin Cities, we stopped at Rockler and picked up some quarter sawn oak - 48" long by 4-6" wide, sequence matched. Came in a 12 sq foot bundle.
My cabinet that I posted a picture of above needs the entire top veneer replaced. Other than that, the cabinet is in near perfect condition.