I'm not sure if there is a specific thing they do for birthdays, but they will probably give each of them an "It's My Birthday" pin, and the more they wear it over the day, the more little perks other CMS might (and I stress might). They will possibly offer a special little dessert for free.
If you want to make sure something special is done, you can order a cake ahead of time. Did it for my fiancee-now-wife on our last trip on her birthday. I forget the number but 407 WDW DINE might be able to help.
I was at MGM this past weekend on my daughter's b-day. We had gotten the "pin" at guest services but the response from CMs was pretty weak. A few of them wished her a happy b-day, but it was more in response to the shirt she was wearing that said she had come on her b-day to meet the soap stars, not the pin.
We ate at both the Prime Time and Sci-Fi. No one even noticed the pin at Prime Time. At Sci-Fi I asked our waitress if they still did the shouting thing to the whole restaurant. She said that they weren't allowed to any longer by the "big wigs". That was disappointing to my nine year old daughter, she had really enjoyed it in the past.
The only dessert she got was the sundae that already came with the kids meal. Our Sci-Fi waitress was very nice and seemed a little embarassed about the lack of something special and she did put a candle in the dessert and gave her a card.
I can't imagine why they would purposefully stop something like the announcing of a b-day. I also noticied that the staff wasn't into the movies like in times past. They had always yelled things at certain times of the show, but not this time.
Tell them in advance about the birthdays and they'll do something. When we went last year it was a family friend's birthday and everybody sang happy birthday and made a big deal of it at the 50s PrimeTime Cafe
I ate there during one of my travel companion's birthdays and they passed a card around the restaurant for all the other guests to sign and then presented it to the birthday boy.
I think it really it depends on the waitress or waiter. I went to 50's on my birthday and my gf's birthday. "Mom" made us stand in the middle of the room and had everyone sing happy birthday to us, I also received a card signed by all of our "cousins".
Been there for a b-day before, and they did make some kind of to-do, though I cannot recall what it was. BTW I've had two of the special arrangement cakes (one at the 50s, one at CG) and was a little disappointed, esp. for the money. I'd almost prefer a regular dessert with a candle, but that's me. I'd still let them know when booking, and when you check-in at the desk, that it's for a b-day. FWIW.