Good question, Sharon! And it’s especially timely because one afternoon a few weeks ago, an APCC staffer and her daughter were terrified to find themselves practically face to face with one of these creaturesone of the largest wasps in North America. As they have four dogs and a young child in their family, they wanted to learn all they could about themand were relieved to find that they are not as dangerous as they appear to be.
There are different species of this genus of wasp (Sphecius), living regionally throughout the U.S. The male cicada killer has no stinger, and the female possesses a tube on her rear called an ovipositor (used to lay eggs). She does have the ability to sting (first injecting a paralyzing venom into the cicada, she drags it back to the burrow for her larvae), but will typically not do so unless in considerable danger, i.e., handled roughly or stepped on. They do tend to fly around the heads of people and animals who venture too close to their burrows, which are usually found in dry soil with sparse vegetation; because of their size, this can be quite scary. However, it is more likely that they are either curious, or simply trying to ward off people from stepping on their nests with this "dive bombing" behavior. The good news is that these insects are usually above ground for only a month or two at most, at which point they die off.
Should your dog wind up getting stung by a female cicada killer, see your veterinarian for treatment. Serious problems would not be expected unless your dog happens to be allergic to bee or wasp venom; in that case, we would recommend taking your dog to your local clinic for treatment right away, as significant allergic reactions can become life-threatening.
For more information on these unique insects, visit Professor Chuck Holliday's Cicada Killer Page. This entomologist from Lafayette College has a lot of information that you may find helpful.