Q: I have upgraded my iphone to ios6 but I can't see facetime application. Why?

FaceTime is only available for the iPhone 4 and above, mostly due to a front-facing camera as a limitation. I've heard word that people have jailbroken their phones to use it but I don't see the point since you wouldn't be able to see the screen on your phone while facing it's rear camera anyway.

The iPhone 3GS never had Facetime, and it never will either. Two reasons exist as to why this is: one would be the fact that there is only one of two needed cameras available on your phone, and second is the software on your device that will never change to add Facetime. Unfortunately, unless you own anything prior to an iPhone 4, you will not be able to use Facetime regardless of your Operating System (in this case, iOS 6).

The good news: if your plan with your current iPhone has expired, an iPhone 4 would be free of charge if you purchased it with a plan, I believe (although it may very well be different depending on your carrier).

See this support document regarding Facetime http://support.apple.com/kb/HT4319 however, as the previous poster said, it is only available for the iPhone 4 and above. Also, there is no Factime app on the phone, if you have a phone that supports Facetime, other than having to activate it in Settings, the only way to access it is in a phone contact.

There never was a Facetime application on the home screen of the iPhone. It has always been accessed via the phone contacts.