When you run, don't be afraid to put a lot of space in between the limbs. You need to do this so that he moves faster.
You probably notice in the 3rd image the arms are almost in the same spot. You need one frame like this so that it looks like the arms are crossing each other. If you don't make a frame like this it will look like this:
It is like as the arms reach to the chest, they stop and go back to the first direction they were going. You don't want this.
One more thing is you need to bend the back. Look at the previous animation, another poor thing I (purposely) did, was not bend the back. Doesn't it look funny? When you animate a run, or even a walk use at least 2 joints and bend the back. Some people bend it a lot, some people don't, but just bend it however much you think looks best. When you are making a walk it probably shouldn't be bent as much. Here is an example:
There is a jolt in this loop, sorry about that.
Notice how far out the front and back legs go. They should both be in the air for 1 or 2 frames. I really haven't figured out how to make it in the air with only 1 without getting yelled out for not easing. Lol.
And last but not least, the key to getting good at running and walking, practice a lot, until you get it just right.
Anyway, this is all of my knowledge of running, I hope I could help you. =D
Anyways, awesome. Thanks for this, I can now walk and run on pivot easily, too bad I quit. I want a new one from you Jdogg. Remember that movie one you made? How about another one?