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I know this could go in equipment, but it has to do with training.
MAKE SURE YOUR SHOES ARE FOR YOUR TYPE OF ARCH!
I got medium arch shoes when I actually had a high arch...apparently I walk weird when being watched, which is how they figured out which arch I had...and I got BAD shin splints. And they may have added to the patellar tendinitis I got that season. Unfortunately, I was running XC then so I ran nearly 250 mi in the WRONG shoes!
BE CAREFUL! MAKE SURE YOU BUY TRAINING SHOES FOR YOUR ARCH!

Also, here's another thing:
Unless you jog normally on a treadmill, don't trust the shoe people when they say "oh, well, you ran this way on the treadmill" [if videotaping on treadmill.]
I did, even though I thought that bc I had a high arch I needed a high arch shoe...they said "well, you need a medium arch shoe with this insert." I said, "Well...I wore medium arch shoes last time and I got bad shin splints..." "This is what's best..." "Okay..." and I got them...I got shin splints within a week or two. We took them back and got the shoes I originally wanted...I haven't had shin splints since.

Also, I have nothing against spikes if you don't wear them for normal training...you'll beat up your shins if you wear them for training bc they have little padding. [I LOVE my spikes...but I only wear them at meets for that reason.]

I disagree with above, although shoe choice is important many research studies, (I have none i can post right now but I will try) show that many foot and shin problems can be solved or at least helped with less footwear. Nike noticed that great distance running countries with little money to buy shoes generally have the strongest feet and little foot injures because they run barefoot. Now because nike sells shoes they, sold you a flimsy "nike free" telling you it would get your feet stronger, for $100 a pop it does, meanwhile kenya just walks around without shoes.

If you can incorporate barefoot training and running into your daily regiment (for example running your warmup barefoot), expensive over thinking of shoes and arches can be bypassed with the strengthening of your feet/shins. This is not a silver bullet for shin splints but it has been seen to be generally true.

Running track and pole vaulting does take a toll on your shins, so strengthening your Tibialis Anterior is just as important as strengthening your core or biceps.

My knees got messed up the most.
Plus, I have high arches.
I know that it can be helped by strengthening those muscles, BUT, at the same time, you don't want shin splints while training.
So, for training, IN SEASON, it might be best to have good shoes.

one thing to keep in mind

running in bad shoes is a different animal entirely.

i do a lot of my running barefoot to strengthen those muscles, but if your running in shoes that aren't designed for your foot/stride type, you can certainly do damage to many joints/ligaments/ etc

A lot of it is genetics IMO. Some people's shin bones have irregular curves in them causing more stress than usual. Obviously strengthening all the muscles helps, but unless you begin strengthening when you are young im not sure how much result you would see. I'm also not sure that in kenya and other great long distances running countries, its not survival of the fittest!! If you cant run with bare feet without getting shin splints, you die! Hence on those with good genetics move on to repopulate.