Do people who were born on February 29th celebrate their birthday every four years on Leap Day or do they celebrate their birthday on March 1st each year?

Well, it would be more logical to celebrate it on March 1 since it's the day following February 28. But to be safe, just celebrate on both days like what I do :)

In cases of New Zealand citizens, the NZ Parliament has decreed that for a birthday that falls on February the 29, and is not a leap year, the legal birth date date shall be the preceding day, the 28th.

I was born on February 29th, and I celebrate my birthday on February 28th and March 1st, and every actual February 29th I have an especially big party.