Tucson Area Hiking Clubs
The local chapter of the Sierra Club (the Rincon Chapter) leads hikes in the Tucson area, and you don't have to be a Sierra Club member to go. A list of the upcoming hikes can be found at the Sierra Club website.
Southern Arizona Hiking Club
The Southern Arizona Hiking Club (SAHC) leads hikes almost every day of the week. They publish a bulletin which lists all of the hikes, and to get the bulletin you need to join the club. To get a membership kit, including an application, go to the SAHC website.
Ramblers Hiking Club
This is the University of Arizona hiking club.