My dog does the whole running whilst lying down thing but not then getting up and running into the wall (although she has done that a few times awake...)
Going from the experience of watching mine:
Sucking on their mothers teat,
Chasing something,
Happy times, with the amount of tail wagging mine used to do,
Occasionaly something nice to eat given the chomping and slurping noises she made.
Normally mine is just a little paw twitching and occational running, but about a year ago she caught a rabbit and for a few nights she was running like crazy...