No, there is no way to count users of Ubuntu. There are sources from which you can extrapolate more or less realistic estimates, though. For instance, the number of users of Ubuntu One will be known to Canonical, and I'm sure their services are able to identify clients, like any other. They're also opening a lot of shops in China that will sell computers with Ubuntu preinstalled. That's another reliable number. Then you have the software center, where you need to have an account in order to either purchase software or rate existing software. All of these are reliable numbers for a minimum number of users.

The real number can never be known, since Ubuntu is free software and doesn't come from one source. For instance, when I download a new CD image or updates, I do that from the University of Oslo. I don't think it's very important to know the exact number of users, though there is a prize for user # 200.000.000: he or she gets a lot of free software! :)

Hardly anyone knows the real number of users of their services, though. Skype, for instance, is said to have 5-600 million users or something, and about 100 million active users. I haven't used Skype in about ten years, but I'm sure I'm being counted as a user anyway. In other words, such numbers are never entirely reliable. They do portray the situation in their own way, however, and as long as you understand the nature of these numbers, they do tell a story.