Ummm ..... Don't you mean 'What items canNOT be on the table ....'? I suppose there's no easy answer for that one since everyone will have a different take on it. However I would think that we wouldn't want to try to legislate personal items or step upon the rights or customs of individuals. I would hope however that the play space wouldn't become too crowded with personal items, especially such that it hinders the opponents to see one another. I would discourage use of a damage type chart, or other hints. Other than that, I would tend to vote against morally objectionable material or items and such, but be willing to overlook most other stuff if I thought there was no harm done.
EDIT: Please take my response as an answer to what can be on the table during a TPCi sponsored and sanctioned premier event. What happens at league or non-sanctioned events may be entirely different - and is of course not expressly covered by this forum.