Pretty common. My beagles love sticks. I think that they're a common dog toy; I have pictures of my grandma's little mutt merrily running around the yard with a stick 4 times longer than he is. As long as they don't eat whole pieces that they can choke on, as long as they don't chew them into little pieces into your carpet or on your furniture, most sticks should be fine.
As were walking Murphy loves to grab a stick, twig or pine cone. It's a hoot to see how proud he is when he's carrying it, and how bummed he is when he drops it and we're going too fast for him to snatch it back up. He looks back like he's lost his favorite toy.
my dogs dont show much interest in sticks per se, but in their yard are some trees with low branches. they first strip the branch of leaves and bark (over time.. say 10 days) then start chewing the branch up from the end til it is gone. then move on to the next one.
Dogs are just plain wierd.
Jersey loves sticks. Not as much as when she was a puppy though. She used to find one to carry around on our walks. She'd always stop at the same place to find something to walk around with. Silly girl.
Buddy loves the twigs also. He will sit there and just chomp away. He doesnt actually eat them just chews on them. I also have little tree bushes in my backyard that he loves to chew on and rip branches off.