One of the local radio stations used to have a show called Big John and Sparky on weekend mornings. They did a variant of the one Animaterra cited:

[To the tune of the Merry Widow Waltz]

Happy birthday, Happy Birthday, Just for you;
Happy Birthday and may all your dreams come true!
When you blow out the candles, one light stays aglow--
It's the sunshine of your smile, where-e'er you go!

I have used this one at numerous public events, including a hundredth birthday party. Generally when leading it, I line out the song after presenting it once around solo. The words seem memorable enough that the audience seems to pick it up very quickly.

I also find it amazing how many people come up to me afterward and remember hearing it on Big John and Sparky. Once, I was one of the kids they dedicated it to.