I see a lot of kitchen and bath sinks with slimy food residue buildup in the tailpiece and overflows. Many people who use a garbage disposal have this problem with buildup inside the chamber of the disposal. You may try an enzyme formula buildup remover that will help cut down on slimy buildup, or put some powdered baking soda and vinegar down the drain. Personally I like Dave's answer to the the problem be sure to check for proper venting. A quick check that I do is fill the sink to the top with water and let it drain. Often those "vent challenged" fixtures will make a "glug, glug" sound as the air and water try to change places rapidly. Also check under your sinks and counter tops for leaks from the waste line and supply pipes. A small leak could be causing mildew in a hidden area.