This is doable using OpenID Connect, however it's sort of experimental, so details could change in the future. If you get an OAuth token for the 'https://www.googleapis.com/auth/userinfo.email' or 'https://www.googleapis.com/auth/userinfo.profile' scope you can use it to get user info from https://www.googleapis.com/oauth2/v1/userinfo (including email). Of course the user needs to authorize this.
You should theoretically be able to get the token from AcccountManager
using the "oauth2:https://www.googleapis.com/auth/userinfo.profile" as the token type, but that doesn't appear to work on my device (Galaxy Nexus with stock 4.0.4). Since getting a token via the AccountManager
doesn't work (at least for now), the only reliable way is to use a WebView and get one via the browser as described here: https://developers.google.com/accounts/docs/MobileApps
There is a demo web app here that does this: https://oauthssodemo.appspot.com
(late) Update: Google Play Services has been released and it is the preferred way to get an OAuth token. It should be available on all devices with Android 2.2 and later. Getting a profile token does work with it, in fact they use it in the demo app