Unfortunately, many people, including some professionals, believe that in order to achieve stability, you need to perform exercises while standing on a Bosu, or wobbleboard. This unfortunate mindset is preventing SO many people from achieving levels of strength that will improve their stability. In addition to this, when people exercise on Bosu's, they are often reinforcing horrible alignment and poor biomechanics, and will be using significantly less weight than if they were doing the same exercise on solid ground. This will make them weaker AND less stable.
One other thing. Many people suffer from tight muscles. When your muscles, or a single muscle group, is weak, the antagonistic muscle group will often tighten up to provide your joint with the stability that it needs. This will cause discomfort, alignment issues, and many other symptoms or injuries. What you will find, is that when your body is strong and stable, you will no longer experience the same degree of muscle tightness or dysfunction, and you will be able to achieve and then maintain proper alignment.
When your body is unstable, increasing the load, or performing repetitive activities like hiking, jogging, cycling, etc, will reinforce your poor biomechanics and alignment, and will lead to discomfort in the muscles, joints, tendons/ligaments, and can result in both acute and chronic injuries. Before you perform these activities, you need to achieve a strong and stable base. This will save you a lot of grief (physical, mental, financial) in the long run.
I think I'm a pretty good example of what you can achieve when you have a body that is stable. Before, thanks to my severely misaligned ribs (and all of the injuries/issues that resulted from it), I was the poster child for an unstable (and severely twisted body).