Studies show there isn't one single muscle that works the most or the best to hold the spine stable. That means it's likely a single exercise isn't going to give you what you are looking for. If you really have to choose, it looks like the abdominal muscles work the most often throughout spinal movements and trunk stability.
A recent study at the University of Waterloo in Ontario, Canada, showed the importance of all the muscles. They found the muscles change how they function depending on the activity or movement. Some muscles have several different jobs to do and respond according to the activity at hand.
This research supports the idea that many different muscles must be strengthened for good back strength and spine health. The key to successful exercise is find what works for you and stick with it. Consistency is just as important as what you do when you exercise.