The example you will see a lot at the moment is the ASP.NET MVC framework. It is amazingly extensible but that is its downfall in some respects, there isn't any meat to it. Want to do data access? You'll have to write that yourself. Want some AJAX going on? Ditto.
However, as it is highly extensible, if you build upon it you can turn it into an opinionated framework. This is what the likes of MVCContrib do, they give you specific methods of doing things which means you have to write less code.
This does mean that if you want to break from the opinion there is often more work to do than if you were working on the vanilla version. This is an 80/20 scenario though. If you chose your opinionated framework correctly you will only want to break from the opinions 20% of the time and you'll be highly productive the other 80% of the time.
