Is it possible in Silverlight (I can use SL4 OOB if required) to copy/paste into my application? It appears I can only copy/paste text (from what I read)?
It is possible with Silverlight 4 but only for Unicode text (Remarks in msdn documentation). If it is enough you can read this article.
If you want different content you could try using COM object (requiers OOB, tutorial) as described here (its not for Silverlight and it's ActiveX but idea is the same).