You wouldn't dance the Nutcracker in hiking boots, and, similarly, you shouldn't hike in slippers. The most important thing to consider with hiking boots is their stiffness. You may be able to get away with wearing your running shoes or trail runners on day hikes, but with your mobile hotel room (i.e. your backpack) pushing down on your back, you'll need something that puts a little more stiffness between your feet and every rock in the trail. Also, your ankles were built to support the weight of your body; not the extra weight of your pack. So, they'll need some support in the form of a high-top boot -- one that comes up over your ankle bone and, in a sense, splints your foot to your leg. A high-top also keeps debris like dirt and small rocks out of your boots -- debris that could rub blisters.
Of course, even within the category of stiffish high-top boots, there's a whole spectrum of options, ranging from a summer hiker make of nylon, Gortex and suede, to a crampon-compatible mountaineering boot [source: Appalachian Mountain Club]. Now's the time for realism: What kind of backpacking are you really going to do? If you're carrying a light load over a short distance (say less than 30 pounds/13.6 kilograms over less than 10 miles/16 kilometers), you may be able to get away with a sole that has some bend. If you're carrying a load of more than 50 pounds (22.6 kilograms) for a longer trip (and especially with off-trail hiking), you'll need a boot that makes that distinctive "thunk-thunk" sound -- without much flex in the sole. A stiff sole saves your feet from feeling every bump in the trail.