My gramma is an antiques dealer and I've asked her about water spots before. She tells me it depends on the finish and the wood.
If it's old fashioned varnish and the ring is just in the varnish, sometimes a BIT of white vinegar on a rag will wipe it out. If it's thin varnish and the ring has stained the wood, then vinegar can make it worse (e.g. oak will darken).
With newer urethane finishes...well, she hates urethane and won't discuss it.
She ALWAYS recommends testing any method on an area of the finished wood that won't be seen, like on the back.
She's also had me use mineral spirits or even turpentine to get stains and minor scratches out of varnish. I think one of them melts the finish a bit so it sort of spreads out again.
Then she asks me if she should send me more coasters and doilies so I don't mar my furniture anymore. Gotta love grammas.