It looks like the Facebook rumors won't die, and are stronger than ever with the social network inviting the press to an event at the Facebook HQ on April 4th, to "Come See Our New Home On Android."
It looks like the Facebook phone would run a modified version of Android, and may be built by HTC. If the April 4 event does see a Facebook phone unveiled, it'll be an interesting future for Google. Google allow manufacturers to modify the stock look and feel of Android, but the rumors with the Facebook phone are looking to have the Facebook phone see a huge change in the look and feel of Android - which we should expect.
Facebook have a slew of features and apps that they could bake directly into their phone, which would essentially just be a basic Android handset, powered by Facebook. Then we have to wonder about Facebook's App Center, which links to both the Google Play Store and Apple App Store. Then we have to think deeper again, with carriers' opinions on a Facebook phone. I'm guessing we'd see Facebook heavily, heavily subsidize this bad boy, and sell it online and unlocked, ala Google's Nexus 4.