Are there virus free operating system?

Actually, Yes.

There are many operating systems out there which have no possibility for a malware to be written.

THESE CAN AND WILL GET VIRUSES:
Microsoft Windows is a real disadvantage in this, as any program (including malware) can be run and installed WITHOUT the user's permission, viewing this website with a bad line of HTML code will (theoretically) destroy your windows PC.
Linux is like this as well, however there is a real lack of LINIX programmers, sunce there are so many adaptations of LINUX around and thee tiny market share they own.
Most Smartphones: These will get viruses as quickly as windows will, for owners of S60 (the most used smartphone in the world) this is a severe problem.

THESE MIGHT GET MALWARE IF YOU ARE AN IDIOT:
Mac OSX: Mac does not get malware simply from viewing a site, but DO get malware if you really go out of your way to put it on. You will have to manually download a file from somewhere (an untrusted site), wait for the download, manually install the software, allow extra permissions to the file system, do this, do that... virtually impossible
Regular Phones: These run the J2ME Operating system, which has to be configured to work alike MAC

IMPOSSIBLE:
iPhone, iPad: Software has to be certified by Apple and downloaded from the Apple website. You can't make your own software (unless Apple gives YOU permission for a hefty sum of cash). You can however get malware is you hack (jailbreak) the iPhone with your computer and install a similar operating system

- It is understood that "VIRUSES" are actually a specific type of malware (malicious software) which involved corrupt and coding changed OFFICIAL FILES (totally recoding Internet Explorer 9 to becoming a media Player is an example). I substitute MALWARE for VIRUS as malware is really anything you don't want (like most stuff which steals your credit card details which AREN'T viruses), rather than a specific type of bad software.