The answer should be roughly 1/365 of the Earth's population (more on that below). The current world population estimate from the US Census Bureau can be found at:

http://www.census.gov/ipc/www/popclockworld.html

As of March 1, 2009 they estimate the world population to be ~6,763,611,245 (which we'll call about 6.7 billion). If we assume that births are randomly distributed throughout the year (which isn't quite true), there are therefore about 18.4 million people around the world sharing a birthday each and every day.

As to the question of the distribution of births throughout the year, the number of average births does indeed vary somewhat as a function of the calendar month. According to:

http://www.sciencenews.org/sn_arc98/11_21_98/mathland.htm

"In the United States, the data show a seasonal pattern, varying between 5 percent above and 7 percent below the average daily frequency."

Five percent of 18.4 million is about 1 million people. So we can approximately claim that on any given day 18.4 +/- 1 million people are likely to share that date of birth.

Finally, you may want to check out the Wikipedia entry for "Birthday problem" (and references therein) which describes the mathematical process for calculating the probability that a common birthday will exist in a set of randomly chosen people.

I know personally at least 5 people with this birthday.

So 5. :-)

Really, it's got to be in the tens of millions. Here are three tables. The first lists the number of births by month in the U.K. from 1941 to 2005. The other two are for the U.S. The first is for 1995-1998 and the other is for 2000 (see pg. 45).

I don't know that birth data by month worldwide exists, let alone by day of the month!