Eames Aluminum Group Table  

.
My action office desktop has a round stain (flowerpot?), my lamp covers it just great! It's okay for work tables to show evidence of work being done on them. How much do you clean up a workbench?

If the "problems" are water s...
If the "problems" are water stains, then oxalic acid will make them go away.

Not water spots. More like...
Not water spots. More like permanent marker / ink spots or something.

---
I use hairspray or rubbing alcohol for that kind of thing

I've cleaned it up well...
I've cleaned it up well using mineral spirits but if I try to clean it any further I'm afraid I'm going to do irreparable damage to the veneer. The staining is literally embedded into the grain.
I guess what I'm wondering is, would it look best if I stain it or should I leave it as is? Even from a value standpoint, what's the best route to go?

The best route
is reasonably cleaned up, "as found" condition.

If you saw the original...
If you saw the original condition of this, you would have left it in the trash. The frame was completely oxidized and rusted and the top was dirty as hell, some peeling up of the veneer etc.
The frame now shines brightly and I've repaired the veneer. At this point I've put enough time into the table that I'd like to make it the best it can be since I'm well beyond the "cleaned up 'as found'" route...
So the question still remains, to stain, or not to stain...?

..........
If you're looking for someone to tell you to stain it, perhaps you should just stain it!
My advice is to use good judgement, which I think would probably exclude staining. Post pics if you want better advice?

I'll post pics later...
I'll post pics later tonight. I honestly have no idea what I want to do. Just sort of curious since once I poly the top, all the imperfections are there to stay. Whereas if I stain it before poly, some of the imperfections will be dulled...

Try what Leif suggested.
Oxalic acid. Cheap, easy, relatively safe, and remarkably effective at making those blue-black iron stains on oak disappear like magic. Totally worth a shot if the veneer is otherwise in good shape.