Shields UP! Link: Click here (opens in new window)
This is a website that checks your computer's internet security. At the start of the check, it displays your "reverse DNS". It can check the visibility of the ports (ports 1-1056) on the computer (or other device that is connected to the Internet), providing information on the status of ports that are visible to anyone on the net.
The 2 computers that I tried this tool returned "TruStealth" status (henceforth referred to as A & B), i.e. there is no indication that the computers used to access the Internet were visible in any way. This includes not responding to Ping requests generated by the test site (which is "cool" as they say). According to the website, stealthed ports required more time to complete analysis as more packets were sent, to make sure packets were not dropped.
For testing's sake, I ran an FTP server on Computer A, and only then did the refreshed page show an open port on that computer.
However, the port scan is still incomplete, as another scan by Symantec Security Check (apparently using ActiveX controls) on Computer B returned different results. The Hacker Exposure Check here showed that the port "ICMP Ping" is OPEN, while Shields UP! said that no response was taken. Other ports such as 1723 PPTP (Point-to-Point Tunneling Protocol), 5000 UPnP (Universal Plug and Play), 5631 pcAnywhere, and a range of ports above 1000 were deemed closed by this alternate tool. These ports were not covered by Shields UP!, and hence it may not provide an accurate total overview of the security of your system.
Definitely worth a try.