Updated with data from september 2014
There is no way of knowing exactly how many people use GNU/Linux nor how many computers run GNU/Linux desktops. That's the whole point of freedom, users don't have to tell anybody that they are using a free OS, users do not register and nobody is tracked. It would be interesting though to know roughly what order of magnitude we are talking about and there are some statistics that can give us a hint. The main statistics we have are Linux counters (see links below) and the percentage of GNU/Linux operating systems browsing the Internet (see links). These shares and trends are all predictions but anyway, interesting to take a look at.
Linux counter guesstimates about 73 million users based on circa 130.000 registered users (linuxcounter.net, 9/2014) but this number is only an estimation based on users that are actually registered on their site. They believe that between 0.2% up to 5% of all Linux users are registered on their site.
The average of Internet browsing statistics from several sources estimates that GNU/Linux operating systems represent 1.67% of the total web traffic. If we add Android to this number (since Android has a kernel based on Linux) then we have 19.56% of browsing share for Linux all together. This number vary from 1.49% for StatCounter on august 2014 to 5.6% for w3schools for the same period. Gartner expects the GNU/Linux share to remain under 2% for the next several years (gcn.com) but says that, in the cloud era, Linux will prevail (and it won't matter what OS you have on your desktop anymore - link).
This is a pure guess but we could say that there are approximately 2 billion computers in use today (about 1 billion in 2008 and an estimated 2 billion by 2014 according to Gartner). In this case the 1.67% of GNU/Linux computers browsing the web would be something like 33,400,000 or more machines. Counting Android devices this number jumps to 391,200,000 or more Linux-based operating systems browsing the web.
There are interesting data regarding the shares per country and per region. According to Pingdom in 2011 we have: Cuba, leading with 6.33% GNU/Linux shares in their own market but South America with only 0.88%. Macedonia is the leading European country with 2.8% and Europe altogether is the leading region with 1.14% according to StatCounter alone.
Another difficulty is that we have no way of knowing how many users there are for each computer. Sometimes one computer will be used by an entire family, sometimes one individual has an entire family of computers. We also have to consider that most GNU/Linux users have another OS available and might use it to browse the web.
The increase of registered users at linuxcounter.net are of about 15,000 users per year, meaning that it could be a total increase of 600,000 new users per year.
The browsing trends are really hard to follow but most of them show a global increase of GNU/Linux OSs. From the different sources of web statistics we observe that GNU/Linux shares increase roughly from 0,1% (netmarketshare.com) to 0,5% (w3schools.com) each year. This increase could be from new machines entering the market as well as old machines switching to GNU/Linux. There is no point, really, in trying to know exactly how many users there are, but while we're at it, let's do some wild predictions!