I use a shotgun and an electronic caller with a variety of calls. "Death Cry of a Crow" seems to be the most effective, and will also bring a fox occasionally. "Hawk and Crow Fight" brings them in too, along with the occasional hawk. Sometimes they bump into each other before they reach me and take off fighting, leaving me feeling just a bit left out.
A good tactic is to stand next to a conifer or other cover, so the birds can't see you until they are in range.
The real fun comes when you engage a crow in conversation, with him a little closer each time he caws. Crows are quite intelligent, and fooling them isn't easy, especially late in the season. The look on his face when he pops over the hedge and sees the shooter is priceless.
A crow is as big as a pheasant, but not nearly so tough. No. 6 shot works well for crossing shots, and 7 1/2 is fine for incoming shots. I like an improved cylinder choke in the fall, but might go to a tighter choke after Christmas.
Rifles are legal for crow in Missouri, but the wing shooting is so much fun that I've never bothered with rifles for crows. I am told, however, that the .17 HMR is a 200 yd crow killer.