From the "how many times have you downloaded it?' files:

Mozilla's Firefox is nearing a major milestone - 1 Billion downloads. That's BILLION with a B.

Now that's not a billion users, mind you it's downloads and hey who among us hasn't downloaded Firefox more than once?

There's a counter up on Twitter, updating every five minutes or so. The tweet i saw was:
999,024,648 downloads at 20.3 per second on 2009-07-30 21:09 UTC.

It's a major milestone for sure.

In terms of how many actual users Firefox has that number is somewhat smaller. In May, Mozilla reported 270 million active users.