You need to name a cruise line as they all offer different packages.
Can't comment on other lines but my parents were on a world cruise last year with P & O for their wedding anniversary and a birthday. I was able send them flowers, champagne and have cakes made on both occasions, once to be given to them by the waiters singing to them at dinner and once delivered to thier cabin. P & O have a huge brochure to chose from for gifts ranging from the above to spa treatments, photo's even cuddly toys!
Agree with Bailey. We were on the Oceana in April. We ordered a cake and got the usual waiters song around our table. It was my husbands birthday on St. Geoges day. He nearly slid under the table with embarrasment, because he always said Dont ever do that to me. But you have to dont you? What amazed us even more was when we got back to our cabin there was asigned birthday card from the captain and a delicious plate of petis fours! Well done P.O. Probably other cruise lines do something similar. It all makes things that little bit more special. Have a lovely cruise whoevers birthday and whatever ship.