Running babe (and husband) have acquired a new puppy! It was not a requirement high on the list but I really wanted a dog that I could take running with me. I know that no dog will want to do 10+ miles, but I would feel a whole lot safer if I could have one with me when I do early morning or evening runs.
Our dog, a Rhodesian Ridgeback (possibly mixed with boxer) loves to run. Though we'll need to wait until he's at least a year old until we go out. His bones and joints need to reach full maturity before he takes his momma for a run!
Other dog running tips:
-be sure to not run them too hard or too far, build them up in mileage just as you would any new runner
-make sure they get plenty of water, frequent rest stops are a must
-Make sure you're not running them in too hot or too cold of weather. Remember they have fur (hot) and can't sweat (just pant). But they also have exposed paws that can get cracked if they get too cold.
-always run them on a leash, dogs like to chase by nature (cars are not excluded)
Here's a list of good breeds to have as running companions.
Some other good dog exercising tips.