On 8 Apr 2007 01:05:31 -0700, "riverman" wrote:

I'm a novice and newbie, so go easy on me, please :-)

Some houseguests have left serious white rings on our wood dining
table, and they cannot be buffed out with various methods (toothpaste,
furniture polish, light sanding, etc), so I think I'm faced with doing
a repair job. I have previously sanded and varnished a teak picnic
table, but never a nice dining room table. And because I really like
the old character of this table, I'd prefer to just repair the rings
rather than redo the entire top.

Try Liberon Ring Remover:

http://www.rockler.com/product.cfm?page=6517&cookietest=1

Instructions are on the Rockler page.