As someone who ran ~ 40 - 45 miles a week consistently for over a year and a half (prior to my introduction... or maybe indoctrination into T-Nation), I hopefully can shed some light on this.
Most people (I'd reckon 90% of the people I used to see on my runs) have terrible form. I never once experienced any shin splints or injuries. I logged over 1500 miles total in a year's time.
The first thing is to become conscious of your running form. I know this sounds so cliche, but I believe that is the key to solving most problems. Pick up any one of the running magazines and just glance through it - almost every issue reiterates proper distance running technique.
Secondly, a good, high quality pair of running shoes. Cross-trainers won't cut it.
Lastly, go see a doctor if the pain persists. For me, once I started seriously squatting and deadlifting, I simply couldn't run the distances I used to. I now do 8 x 400 meter sprints with 90s rest intervals 3x a week and enjoy it a lot more than those marathon cardio sessions.