(besides creating a dedicated account)
OpenID
A dedicated account (my preference)
If you require Facebook then you're locking me out when I'm at work.
BrowserID is well on our list (Personally I like its approach).
Added a vote for OpenId, and dedicated account.
[1] http://developer.android.com/reference/android/accounts/Acco...
Upvoting GoogleID.
PKI (SSH or similar).
OpenID.
I'm another one for whom FB is an instant no-op.
You should build the best possible product for the platform you are running on.
On Android there is an obvious default choice, and it isn't Facebook, nor is it a dedicated account.
Unfortunately, to chime in on the discussion one needs to log in with Facebook, which might keep a good chunk of those 'Please support something else' voices out. I know you wrote (both here and in that entry) that you plan to support other authentication methods. The reason why I post this is just to point out the flaw of asking the subset that willingly gives out their FB details in the first place.
Can the browser/login be completely removed from the picture, so that you get to manage your own scenarios either online or at home computer and push some compiled file to the phone yourself?