Buteos are broad-winged hawks found soaring thousands of feet in the air on thermals or perched on telephone poles. Buteos hunt mostly mammals but will also opportunistically eat reptiles, amphibians and other birds. Some common include the Red-tailed Hawk, Swainson's Hawk, Rough-legged Hawk, Ferruginous Hawk, Harris's Hawk, and Red-shouldered Hawk.
Harriers are also called Marsh Hawks. In Wyoming, we have one Harrier called the Northern Harrier.
Northern Harriers are a medium sized hawk with a long tail, white rump patch, yellow eyes and a facial disk which increase their sense of hearing, similar to owls. They are found in open country such as prairies, grasslands, and wetlands.
Accipiters are the sprinters of the raptor family, they are faster even than falcons for short distances. They hunt mostly song birds. Accipiters are found in forests and have distinctively long tails used for steering around sharp corners. Some accipiters found in Wyoming are the Northern Goshawk, Sharp-shinned Hawk, and Coopers Hawk.
Here's an amazing video showing the capabilities of an accipiter, the Goshawk: