Nobody knows quite how many there are, though there has to be more than just a few million. The problem with more and more computers connecting to the Internet is that as more devices (cable modems, ADSL router etc) require a permanent, fixed IP address (basically a unique "address" for each computer, so that one computer on the internet can route its communications to another PC instead of it just floating about in the ether). The existing IP address scheme, IPv4 (a number with four decimal points in, with each group of numbers between the decimal point having a maximum of 3 numbers, up to the value of 255 - eg. 192.168.1.20), was thought up over 20 years ago, and is beginning to show its age. It gives us a maximum of 4.2 billion useable addresses. This is why IPv6 is beginning to rear its head (a new, fresh update of the IP scheme, which uses 128 digit IP addresses instead of the 32 digit ones that the existing IPv4 uses). I quote, from www.crt.net.au/etopics/ip.htm (because it says it so much more eloquently than I could); "IPv6 is designed to resolve this performance issue along with other problems by increasing the possible number of numeric addresses. This won't be a small increase. It will multiply potential Internet addresses by a factor of 80 octillion or 80,000,000,000,000,000,000,000,000,000. With IPv6, the number of available addresses will jump to 340 trillion trillion trillion." That's quite a few. So, while we may never know just how many PCs are connected to the Internet (because it's impossible - at present - to count how many PCs are connected via proxy servers or firewalls in businesses and in the home), we know that once IPv6 becomes de facto throughout the world, we'll certainly have a few free IP addresses to spare for the next few hundred years. ;)

You could make an educated guess based on many sources of info but you could never say absolutely, with certainty, that "there are X number of computers right now connected to the internet". The only way to do that would be if every time a computer was connected to the internet automatically sent out a message to a central database to log itself with it's unique ID, type of device, and time that it connected. You would also have to ensure that every node device had this feature built into it and wasn't hacked into. I can't think of any info that's currently available on any server that logs every time a computer connects to the internet. If there was, then it would also show computers behind firewalls, that are otherwise hidden, unless you hacked into the firewall to see how many internal IP adresses were active to count them also.