One of the reasons that Angry Birds is such a success is that it just feels good to play. Particularly on touchscreen devices, the feeling of pulling back the angry bird and letting 'er rip is uniquely satisfying.
But even a touch screen is no substitute for actual tactile feedback. If you use this tangible controller cooked up by some students at the Copenhagen Institute of Interaction Design, you'll have all the tactile feedback you could desire.
I mean… just look at it! Check out the little TNT detonator! I.. really want this. Too bad there's only one.
You can find out all about how they made it at the controller's project page.