Most toe problems you're going to get while running or hiking will be cosmetic rather than serious. The most frequent visitors with be black toenails, which are so linked with running that the condition is known as runner's toe. Runner's toe happens when the nail is either pressed down too much on the bed that underlies it or the nail separates from the bed. In either case, blood pools between the nail and the bed. Eventually the nail turns black.
When this condition is caused by the nail being pressed into the bed, it's almost never painful. The nail gets very hard, and it looks like hell, but it won't bother you. After a few months, the nail will grow out and fall off. In the meantime, you've got yourself a nice little memento from your miles that will instantly identify you as a runner to any knowledgable person who happens to see your feet.
Sometimes, the nail loosens rather than hardens, and this is usually uncomfortable. New runners whose toenails aren't used to much wear and tear will get these more than longtime runners. If your black toenail is wobbly, sterilize a needle, and then use it to drain the blood from under the nail, as you would drain a blister.
Runner's toe is usually caused by ill-fitting shoes. If your shoes aren't long enough, your longest toe (which in some people is the second toe) will slam against the front of the shoe. You might also irritate your nails by running on a course that has a lot more downhills than you're used to, because your toes are going to rise up a bit more than usual on the downhills to help you brake. Wet shoes, either from sweat or rain, are also a leading cause of runner's toe.
Poorly fitting shoes may also cause blisters, "hot spots," and other irritations on the tops of your toes. When a pair of shoes causes blisters during your first few runs, then you've probably bought shoes that are too small. Cover these irritated spots with one of the many second-skin products on the market, and you'll usually be fine.