I used to think that carrying trekking poles wasn't worth the bother. Then the knee I injured in my teens got a little worse, and suddenly a good trekking pole became my best friend for navigating steep downhills at speed.
Do you absolutely have to have a pair of trekking poles along to hike? Nope! But you also don't need to have a bad knee to appreciate their usefulness. Here are some of the other benefits you can get from keeping a pair of poles handy:
A Power Boost
Ever wish you had an extra set of legs to help power yourself up steep hills? Shorten your trekking poles up and you can use them to power yourself uphill with your arms, taking some of the strain off your legs while you're at it.
In an emergency, your trekking poles can form the frame of an emergency shelter. (You can use them to improvise a splint, too.) Some hikers go one further by carrying a tarp or tarp-style tent that uses only trekking poles and guylines for support; no tent poles needed. All things being equal, any opportunity to exchange a single-use item (tent poles) for a multi-use item (trekking poles) is a win.
Some folks really benefit from the extra balance and stability that trekking poles provide, especially when traveling on uneven terrain. Poles can also make it easier to balance when you're hiking with a big, heavy pack -- but keep in mind that if you can't balance your pack without the poles, there's something wrong with it. Either it's too heavy for you or it's packed incorrectly, or both.
They're Good for Poking Things
The wilderness is full of things you might want to touch but probably shouldn't. How deep is that mud hole? What's behind that curtain of poison ivy? What's inside that pile of bear scat? If you have a hiking pole along you can use it to poke and prod to your heart's content, with no worries of losing a boot, getting a rash, or getting your hands... icky.
The nice thing about modern trekking poles is that they're almost all adjustable. So when you don't need the poles, you just collapse them, stick them in your pack, and carry on with your hands free.