The oldest I know of is with a relative of mine. He runs an accounting company, and they are using a 15 year old IBM minicomputer (a small mainframe - http://en.wikipedia.org/wiki/Minicomputer ) for the accounting.

I asked him once why he didn't switch to PCs, he couldn't see any reason to do so - the minicomputer was rock solid, still running strong and had the software he needed.

I imagine the oldest machines still in production would be with companies that regard computers the way a factory would regard expensive machinery - switching costs are high, and there is no sense in switching when the old one still works.

And I guess they would be mainframe class computers rather than PCs.