Just to present an opposing view, since I appear to be in the minority: I strongly dislike flippy screens.
My definition of usability is if I can use it while wearing my heavy winter gloves, or while flying in a helicopter, or both; I think it's a feature that may look cool on store shelves, but not while climbing a mountain. To me it just seems unnecessarily fragile—the point of a DSLR is to take the picture, in any conditions, and retain as much data from the scene as possible.
That said, I have used the D5100, it's a great camera, and the screen suits the feature-set and design intentions of the camera. The sensor is fantastic, so it's a camera that will grow with the user for a long, long time; the only thing it lacks compared to the "Enthusiast Level" cameras is the controls and a few extra features (like flash commander) that make the camera a better work tool in a dynamic environment.
If you have the time to sit down, plan things out, and shoot fully manual, the D5100 will take exactly the same photo as the D7000, for just over half the cost.
Personally, hold the flippy screens—I'll keep my extra buttons, speedlights, and dual SDs.