Im sure it's someones birthday today. I wonder if there are any days when no one is born?

February 30th

If we just look at the 8 billion people who are alive today, and divide that number by 366 possible birthdays, we get 21,857,924 people on average for each birthday. It would be an incredible coincidence for one of those days to be vacant. And that's not even counting people who have died.

Unlikely.

[c=800000] everyday in a year has same twenty four hours so may be it's possible there will be a moment where none is born and now will die
It's like our world has stopped for a moment [/c]

Nope

Considering how many people there are in the world, it’s unlikely.