Ever heard the phrase 'Junk Miles'. Simply put Junk Miles are the slow plodding jogs you do when you're tired, sore, fatigued, or before and after the 'all important' tempo session. The assumption is that jogging along slowly serves no purpose. I can't stress how wrong this assumption is.
I run every day and have done for almost 800 days in a row. Many days I run twice. I'll sooner do another 50 minute jog then the stride outs or the short reps my program recommends. I'm no great runner (yet) but I believe almost everything I have achieved thus far has been through the constant gradual aerobic work I do while out jogging. I have no special talent or genetic variance that makes me better then anyone else. The truth is that I've just done the work, and the work is seldom hard.
Time on your legs at any speed is beneficial in some way. I figure if you're jogging tired you're training your legs endurance. I have found my ability to run long is far greater then my true speed. Earlier this year I surprised myself by running almost 90km in a little over 7 hours. If someone told me a few years back that such a feat was possible I would've laughed into my pint glass. A couple of days ago I submitted an entry for the Western States 100 mile and I am confident I can run this distance with no specific training other then continuing my constant steady mileage.
Running at any speed elevates your heart rate and regardless of your fitness even a slow jog will have you operating in an aerobic manor. Aerobic work is the core basis for anyone that races any distance greater then 800m, so lets just assume that's everyone. Except for the 1st few hundred meters and last dash to the line all racing is pretty much done aerobically. When was the last time you saw an Ironman athlete doing 400m reps on the track? Chances are you probably never will.
I guess what I'm trying to say is, provided you can avoid injury, run as much as you can for as long as you can as often as you can. Even eroded to a slow jog you are getting better. The advice I give to people who are first starting out is, choose how far you want to run that day and find the pace you can maintain to cover that distance and don't worry about going fast. The next bit of advice I have for new runners is, do a huge stack of really boring but consistent jogging and call me again in 8 months. Greatness awaits only those who pursuit it.