If you don't, the most likely answer is that mice will get into it, which also kind of sucks. This is why shelters are overrun with mice. Sometimes they're eating dropped food, but much of the time they have been habituated to steal food from food bags. Mostly mice aren't lethal, hantavirus excluded. So although we are all annoyed by mice, rangers are not hunting them down with rifles. Bears, on the other hand, ARE lethal. Once a bear has succeeded in obtaining food somewhere, they will return over and over to try again. Which means that if the people before you, maybe long before you, didn't hang their food or did a bad job hanging their food, there will be a bear around to check out your food supply before long.
The reason I care, in addition to liking food, is that I absolutely do not want an animal killed for my mistake. I do not want to be the one who trains a bear to steal food from people. I don't want to be the one who eventually causes a ranger to have to pick up a rifle and shoot that bear. Maybe that bear was a jerk before he started stealing food. Maybe he was already dangerous. But the food is what made that dangerous bear start hanging out around humans. Unconscious humans, usually, as the bears visit at night. Usually they leave people alone, but not always. Maybe they can't get to hung food and they're frustrated. Maybe you smell like BBQ sauce. Maybe other things are going on in their ursine heads. Whatever the reason, sometimes bears attack people instead of just trying for the food bags.
There are some pretty vocal people on the internet who will tell you they always sleep with their food bag under their head and they never have a problem. That's great, until they DO have a problem. They might always drive without a seatbelt, too, and never have a problem until the accident that sends them through the windshield. They're gambling with their safety when they do that. And they're gambling with mine when they sleep with their food.
There are options for how you do protect your food. Personally, I use a sturdy roll top drybag. I have a small bag with a rope attached to it, and I put a rock in the bag so I can use it to throw my rope up over a high branch. Depending on the level of bear threat in the area, I tie the rope differently. If it's low, I tie it off to a nearby tree. If the bear threat is high, I use the PCT method. I'm linking to the Georgia AT club's PDF describing how it works.
Some parks and campsites will have a bear pole to hang from. That's a tall steel pole with prongs sticking out from it at the top. This is a reliable and safe way to hang. Other sites have bear cables, which is a slightly more complicated pulley system. This gets your food way, way up in the air. Mice and squirrels have been known to bypass blocks and get to foodbags on these systems. Additionally, it is possible to hang your food bag from a hook on the bear cables. Then it can be bounced off if you hit the ropes vigorously. If you use bear cables, attach your food bag securely! The third easy way to protect your food is in a bear box, which is a large, heavy steel cabinet that they have lugged out to some shelters. They are difficult to open. As far as I know, bears have not learned how. Sometimes, I haven't learned how, depending on how stiff the handles are.
You can buy a bear-proof stuff sack called an Ursack as an alternative to hanging your food high up in a tree. You still need to secure the bag to something sturdy, like a tree, so that a bear doesn't just leave with it to gnaw on at its leisure. But bears can't get in to these bags. They're made of kevlar.
The last alternative is a bear canister. I myself have not used one yet. They are starting to become mandatory in places due to bear activity. Technically the Ursack meets the same requirements the bear canisters do, but not all agencies have caught up to this message. If you are backpacking somewhere that requires canister storage, you'll have to buy or rent one. If you'll be doing it a lot, it makes sense to buy. I'm including a link to one of the lighter units on the market, the BearVault. At 33 to 41 oz, the canisters themselves carry a hefty weight penalty. But given that bears are intelligent, persistent, and like to teach one another new tricks, bear canisters may be ubiquitous in the future.