As you might have already noticed, the BackGroundWorker class is missing in Windows RT / app development.
The BackgroundWorker was actually just a wrapper for the following class:
System.Threading.ThreadPool.
So the fun begins again with Threading.
The ThreadPool for Win RT is well documented in the Windows Store Apps Development Center:
http://msdn.microsoft.com/en-us/library/windows/apps/windows.system.threading.threadpool.aspx
For those, who like to actually work with an emulated BackgroundWorker, there are also some folks in the web who did build a custom version of the BackgroundWorker like:
http://www.lhotka.net/weblog/CommentView,guid,9cc11080-eeb5-41c0-bde7-b437d28d56fc.aspx#commentstart