Do I Really Need Trekking Poles For Hiking?

A pole (or two) adds stability and a surprisingly good upper-body workout as you use it for balance or to push yourself up and over rocks or slow your descent.
Switch the hand in which you carry the pole to even out the muscle use. Use your dominant, stronger arm for descents or tricky stretches of trail
Take a staff on day hikes if you know the terrain will be rocky, but always take one backpacking for balance compensation.
You can buy expensive, telescoping poles or use ski poles, but you must remove the tips' baskets. Or you can just pick up and do a little whittling on a straight stick you find on the trail.

A hike is basically a long, countryside walk; how difficult or long it is depends on you and what kind of walk you choose. Therefore, whether or not you need poles also depends on the kind of walk you are doing.

For a hike across fairly flat country, with few pitfalls, you can manage perfectly comfortably without poles. Even in more hilly territory, it's more a matter of choice than of necessity up to a point; sticks of any kind (including one snapped from a nearby tree if necessary!) do make hill easier to negotiate and can save you from a fall; but many people find them a nuisance, and if you aren't travelling at a fast pace you shouldn't really need them from a safety point of view.

Where poles are definitely recommended is on steep hills and mountainsides, and also boggy terrain where you can use them to poke at the ground in front of you. In these cases they really make a difference.