I almost always use Auto-ISO. I think it is the best invention since sliced bread, but I also understand why others feel differently. I don't have the D5100, but I do have a D3200 which has a similar sensor as far as high ISO quality is concerned. I use a maximum ISO sensitivity of 3200 most of the time and feel very comfortable about using 6400 in certain circumstances. I also set my minimum shutter speed to 1/125.
That being said, I can echo what the others have said, qualifying their answers about needing higher shutter speeds for action shots and longer focal length lenses. I also concur with what Marty has said about turning off Auto-ISO, or lowering the maximum setting, when you are using flash since it will almost always choose the highest setting in low light conditions. You might also want to read through a couple of the recent posts about flash and Auto-ISO settings.
Marty is also right about needing an almost perfect exposure at the higher ISO settings.