I recently posed this question on a forum, and the answer was worth sharing. (Credit to Raheem Chaudhry)

Take every sperm cell; past, present and future (world ends in 3000 CE) and multiply that number by every egg cell; past, present and future (world ends in 3000 CE) What is that number?

There have been 107 billion people to walk the planet up until now. Roughly. That is according to this article by BBC News. That article was written in 2012, so that also needs to be taken into consideration.

The birth rate for the world is 255 births per minute according to The World Factbook. I'm assuming that the birth rate will be constant, to make the sums a bit easier.

So the total number of humans to exist up until 3000 CE is 107,000,000,000 + (255 * 525949 * 988) = 239,507,591,060 people.
Let's put that to an appropriate number of sig figs.
240 billion people. And that estimate is just for the number of people who have or will ever live up until 3000 CE.

According to Live Science 525 billion sperm are produced by each man in his lifetime. Assuming half of those 240 billion are men, the number of sperm possibly released is
120,000,000,000 * 525,000,000,000 = 6.3e+22 sperm.

However, each sperm needs one egg to fertilise to count as a potential person, right?

But then things get complicated. According to Cleaveland Clinic:

During fetal life, there are about 6 million to 7 million eggs. From this time, no new eggs are produced. At birth, there are approximately 1 million eggs; and by the time of puberty, only about 300,000 remain. Of these, only 300 to 400 will be ovulated during a woman's reproductive lifetime.

Which figure to use? Only ovulated eggs really have the chance to become people. So if half of those people were women then the number of possible eggs is
120,000,000,000 * 400 = 4.8e+13 eggs

For each of those eggs there will inevitably be a sperm to go with it. So there is your answer:

4.8e+13 potential people - in the sense of if every egg that was ever produced and wasn't fertilised, was.
2.4e+11 people - the number of people to exist up until the world's theoretical end of 3000 CE.

Together, they add up to produce 4.824e+13 people and potential people.
Fully written out:

Of course, you could also be asking how many different ways these eggs and sperms can be fused together to form a 'different' person each time. This can be found by multiplying the number of eggs by the number of sperm.

So:
6.3e+22 * 4.8e+13 = 3.024e+36 potential people - in the sense of different combinations of sperm and egg cells to produce new 'potential people'.
Fully written out:

3 024 000 000 000 000 000 000 000 000 000 000 000

3 duodecillion 24 undecillion