Walking sticks can be very useful when walking around the home or hiking in tough terrain. Many hikers use two poles for balance and stability. More modern hiking poles are light weight aluminum and adjustable with easy to hold grips, much like ski poles. A more traditional hiking stick can be heavy and more cumbersome to carry on a long trek. Instead of bringing one of your favorite walking sticks into the back country you can find them as you go and as needed. Here in New England there is no shortage of fairly straight branches that are already dead and down on the ground. Simply break it to your preferred length and keep it as long as you feel necessary. Many times when hikers find nice ones, they will leave them by a trail head for others to use.
If you are walking from your home and not going out for days, then it is nice to carry your own stick. Perhaps you have a collection and grab different ones on different days. They can be made of many different woods, carved, painted or decorated with feathers or other treasures. Hang or lean them by the door so you don't forget to grab it on the way out.
Walking sticks can be useful for extra support and balance. If you are heading up or down hill you can use it for stability or to take a bit of the load off of a bad knee or ankle. They are useful when crossing streams on a log or rocks. They can also give you a bit more security if you run across a dog or other aggressive animal. I like to use them for knocking the spider webs out of my path. Certain times of year they are everywhere and it can get annoying fast to have them across your face, time after time. Other uses for walking sticks or hiking poles are for setting up a sleeping tarp or for emergencies, like immobilizing a wounded leg.
One recommendation is to make sure you have rubber tips on your poles or walking sticks. They can help the base stick securely on rocks, pavement, and so forth. Then they are less likely to slip out on you. If the walking stick doesn't have that you can buy them at hardware stores and slip them on yourself. Usually you can find a size that is close to the size of the end of the stick or pole.
Of course it all comes down to personal preference and how it feels to you. Some will never want to carry extra things, some will find a stick for when they need it, some will need the latest and lightest hiking poles while others don't want to enter the woods without their favorite stick. Give any of these approaches a try to see if it feels right to you, and get out in the woods and enjoy a nice hike.