We've been to WDW several times for birthday celebrations, and yes, on the actual day no less. I have always had it noted when we booked, as well as when booking ADRs. So....first time was back in '99, my dd turned 6 on that trip. She did get a nice birthday card signed by Pooh and friends at the Crystal Palace and they did bring her a birthday cupcake with a candle. That was it for that trip.
Last Oct we celebrated dd's 13th birthday, and her friend went along since she celebrated her 13th the day after we got home from WDW...so moms and birthday girls had a birthday trip. I did mention it when booking at BWV, and at several dining spots when booking ADRs...I think I mentioned it at Crystal Palace and HDDR bookings since those were the spots we were eating on her actual birthday. Oh yeah, also Chef Mickeys for our first meal since we wanted to start the trip off with a bang. CM's brought each girl an autographed birthday placemat, and birthday cupcake. At Crystal Palace, for breakfast, again a cupcake. At HDDR, they sang Happy Birthday to dd...that was her most favorite thing the whole trip...to be singled out by another redhead and have the song sung to her..especially since we were right up at center stage, front row.
The girls did get some happy birthday wishes from CMs and guests alike. But nothing special, like FPs or rides with characters. I did make my own plans though...ordered an absolutely beautiful cake from GF bakery. We had it brought out at the GF Cafe. The whole place sang to dd...she was mortified. David, our server, was a huge amount of fun...he really added to the whole thing.
So...long story short...sure, mention any special occasions when you book. But if you have your heart set on something special happening, I would plan it yourself. Disney just doesn't have the time or manpower to make all our birthday, anniversary wishes come true. In order to do that, they would have to hire a ton of CMs to just take care of proper acknowledgment of guest birthdays. Now, there's a job I would love!!!