As of October 2012, Apple has not released their propitiatory and iOS infused Facetime app for Android devices. I would assume that you will never see such an app from Apple...EVER!
But, Google has incorporated their own 'Facetime' app in the newer versions of their Android OS (Since v. 2.3.4 - announced in April of 2011). This is called Google Talk or just 'Talk' in your app drawer. It is free to use, works just like Facetime but has benefits that Facetime doesn't (or didn't in pre-iOS 6). Here is an excerpt of an article that tells more about it:
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"...The updated Google Talk will let consumers voice- and video-chat with Google Talk users on Android tablets, as well as on computers using Google Talk with Gmail, over 3G, 4G, and Wi-Fi connections. Apple?s FaceTime video chat, in comparison, only works over Wi-Fi connections.
In addition to being more flexible than Apple?s option, Google Talk will also overlay text sent via instant messaging on top of your video chat screen, so you can conceivably follow links sent during chats..."
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You can also turn off the video feature while still in the call and talk voice only and use most of your phone's other functions or apps.
Unfortunately, if your iPhone friends want to video chat with you, they need to buy an Android phone because Talk and Facetime do not work with each other. Simply put, Steve Jobs would never allow the two to work together. He hated Google and Android to the darkest and deepest pits of his miserable and greedy soul. Thus you have seen Apple's failed attempt to create a better than Google's map/GPS app just to eliminate everything Google on Apple devices. It's a hate thing. You might find some kind of hack or crosstalking app in the future, but as for today, you can only "facetime" with other Apple users and you can "Google Talk" with only Android and Gmail users. If you want to cross platform video chat, then listen to the rest of the advice on this blog about Skype, Tango, Qik, or other third party video chat apps.
Personally, I prefer to just voice call someone, get the information I called about and then say "Thanks...Bye!". It's usually even quicker than texting and waiting for a text back. For those out-of-town trips away from the wife, I've done the video chat but both of us have agreed that it doesn't improve our communication any. We prefer to just voice chat only now. Other than that, I have no real need to video chat with anyone. But, that's me. I hope this info helps.