I'm in the process of trying to cull the number of magazines I get. When I am done, Popular Woodworking, Fine Woodworking and Wood will be the ones that are left.
Woodworker's Journal normally has at least one story each month on turning. Fine Woodworking is a high end magazine, although most of their stuff is flat work. For a few dollars a year any of these magazines have good value.
For Arts and Crafts: Sunshine Artist, Craftmaster News and The Crafts Report
For Turning: American Woodturner (does that count since it comes with AAW membership?) and More Woodturning
For wood stuff in general: Popular Woodworking, Woodworkers Journal