What's your hiking style? Your preferred hiking destinations, style and season will all influence your choice of footwear.
How sensitive are your feet? The more sensitive your feet are, the stiffer the sole you'll need to protect them from rugged terrain. This goes double if you're backpacking; you need the extra stiffness to protect your feet as they carry the extra weight of your pack, food and gear.
Do you really need a waterproof membrane? If you often hike in wet or cold conditions, a breathable waterproof membrane will help keep water out and also release sweat as it accumulates. However, when water gets into a waterproof boot, it can't get out -- so the boot will take a long time to dry once emptied. Waterproof boots also tend to be hot and muggy in warm weather, so consider this feature carefully.
Shop later in the day. Your feet tend to swell through the day and on long hikes, so shop toward the end of the day, when you've already been on your feet for a while. Otherwise, your "just right" boots may turn out to be too small.
Wear the socks you intend to hike in. Your choice of socks can make an enormous difference in how your boots fit. If you don't already have socks to hike in, purchase them when you try on your boots.
Put them through their paces. Do your best to simulate real-world hiking circumstances when you try on your boots. Walk up and down inclines and declines with the boots; they should feel steady and stable underfoot, and your toes shouldn't slide into the front of the boot when you go downhill. If possible, find some rocks or other rugged material to stand on to make sure the boot soles offer adequate protection.
Check the heels. Watch out for the very common problem of a too-loose fit in the heel. One easy test is to lace the boots up, then stand up and rock forward onto your toes. If your heels lift up in the boots before the boot heels themselves come off the ground, the fit isn't quite right.
Err in favor of a larger size if you plan to hike long distances. Over the course of a long-distance, multi-day hike, your feet may swell a half-size or even a full size larger than usual. This doesn't mean you should size up from a perfectly roomy fit but, if you're in between sizes, going up is usually the best choice.
Test your boots while wearing a loaded backpack. This is especially important if you typically carry a heavy load; it's the only way to be sure the boots will remain comfortable and supportive when loaded down. Some stores will have sandbags you can load into your pack, or just bring your pack to the store as if you were packed for a trip; the sales staff will applaud your foresight.