On Eclipse - After updating ADT or Updating Google SDK version, we find problem for the existing version of Google Play Service Lib.
From the help of Above answers and other search, found the following way to correct it.
From Project menu of Eclipse, uncheck 'Build Automatically'
1) Delete the existing lib project of 'google-play-services_lib'.
2) Eclipse Menu --> File --> Import --> 'Existing Android Code Into Workspace'
select the project from
'android-sdk\extras\google\google_play_services\libproject\google-play-services_lib'
3) Select the same project by checkbox in 'Project to Import'
4) Also check 'Copy projects into workspace'
5) When the project appears in 'package explorer', right click on it and select Properties.
Select 'Android'
( as solution of 'Gavin Chen' ) - select the latest platform and Api level for this library project and click OK to close properties
5) again right click on same lib project from 'Package Explorer', click on 'Build project'
Now you will find the Google Play Service Library is built properly.
Then you may build your other projects, which are dependent on it. You may also need to 'Remove' and 'Add' the google-play-service_lib, from your project -- properties -- Android -- Library.
You may re select 'Build Automatically' option from 'Project' Menu.