What kind of exercises are the least stressful on joints?

Weightless! The best exercises in terms of least joint stress are those that take your weight off the joints. The most common of these is swimming. The buoyancy of the water helps keep the stress off of your joints. For example, your knees see ~3x your body weight with each step, and the front part of the knee, where your kneecap moves on the end of your thighbone, can see 7-9x your weight with stairs/etc.