What are good neck exercises and back exercises?

See below. The best exercises for low back are gentle core strengthening exercises. A great program for this can be found at www.therehabzone.com.
Core strength. I am a big proponent of core strengthening exercises with roots in pilates. Most back and neck issues are non surgical and can be managed with weight control, healthy eating and living, and cardio and core exercises. Many physical therapists teach basic pilates moves.