There are dozens, if not hundreds, of core specific exercises practiced by exercise enthusiasts around the world. Sit-ups, Russian twists, crunches, bicycles, ab-roll-outs; too many to mention in an article of this size.
While picking the best-bang-for-the-buck exercise would be impossible, as that would be specific to the needs and goals of the athlete, for most people the best place to start is with the Plank, followed by all it’s variations.
When training the Plank it is best to move from stability to mobility. Start by holding the basic Plank position for 15 seconds. Repeat this four times. When this becomes "easy" increase your hold time to 20 seconds, and so on, adding time until you can hold it between 60-180 seconds. Then move on the next variation. Within a few weeks your core will be strong and stable. Then you can really begin to explore all the variations of abdominal training available!