We go every May for our anniversary - depending on where you stay and where you eat - they may or may not do something special. Sometimes they will ask when you make a ps if its a special occasion, but not always. We have mentioned it when making PS and been given champagne on one occasion and desert on this past trip. It just depends on who is working that night and how it is approached I think.
Keep in mind that nothing is ever guaranteed, but if you mention it casually odds are you may get some pixie dust, but the key is not to expect it or be disappointed if nothing happens. Hundreds of people a day probably say its their birthday/anniversary - its hit or miss, but never hurts to drop a hint.
Our server at R&C this May told us a funny story about how the parents told them it was their daughters birthday and she really wanted to sit outside blah, blah, blah - when the cm's went over to take her a desert and sing happy birthday the little girl sat straight up and said, "but my birthday is in December" - this happened about 3 weeks ago!
Melissa