Can I get worms from my dog?

Some (roundworm, hookworm, tapeworm) are and some (whipworm) aren't. If you think your dog has worms, please contact your vet and bring them a fresh stool sample for analysis. If you think you may be affected, you'll need to see your doctor too.

BTW, this is a good time to mention that in addition to avoiding unknown feces and doing regular fecal sample tests, there are preventative treatments for all these worms as well as fleas (which also spread worms) that help avoid your dog & you contracting worms.