Burn marks:

Grind egg shells with pestal/Morter and mix them with real mayonnaise to make a paste.

Using your finger work it into the burn mark.

Let sit for 10 min.  Work in some more and wipe off.

Water marks:

Basically the same idea but use cigar or cigarette ashes with mayo.  Dip a damp cloth in the mixture and work into the stain.  May take several applications.

I have also heard of using 1/2 and 1/2 toothpaste and baking soda but have not tried it.

Preventing water marks:

Put a good coat of butchers wax on the table using very fine steel wool and let it sit and dry.  Buff off with soft cloths.  Several applications build up a protective layer.  I can put a sweating beer on my coffee table and leave it for hours with no damage.