The new iPod Touch and the Mac FaceTime app both allow the user to send and receive FaceTime calls with their email address/Apple ID as the identifier. Is it possible to set up an iPhone 4 to send/receive FaceTime calls with my email address instead of my phone number?
I'm not following why everyone else is saying this can't be done. I have people facetime me all the time on my phone, by using my AppleID email address. I also contact others this same way, and it works just fine. In fact it has the added bonus of ringing ALL iDevices linked to that address. So when someone facetimes my AppleID, it rings on my iPhone, Mac, and iPad all at the same time, allowing me to answer it wherever I am at that moment.
I didn't do anything special to set this up... just went into FaceTime under Settings, and added the email address(es) I wanted people to be able to reach me on. Works fine.
Maybe this is specifically a problem on the iPhone 4 as opposed to the 4s which is what I have?
On the iPhone itself, you are unable to add "e-mail address aliases" like in the OSX App. The only method of having people call your iPhone is by giving them your phone number.
As far as the iPhone making facetime calls, the only easy way I've seen to do it is to already have their Facetime address in your Address Book, or use Safari.
Open Safari on your iPhone, go to the URL bar, type:
<facetime://firstname.lastname@example.org>, then tap the "Facetime" acknowledgement button afterwards.
I think email address is the only way to do it.