When most people say "core," they mean the abdominal muscles, but the full core actually includes any muscles and structures that support and stabilize the pelvis, spine and shoulders.
With this definition in mind, exercises that control movement, specifically extension, flexion and rotation are solid options.
So while we train most muscles to move and accelerate, we should train our core musculature to decelerate, control and transfer movements—that means lying down and pulling on the back of your head to facilitate cervical and thoracic flexion (i.e. sit-ups) may not be the best option.
Controlling for factors like a healthy diet and genes, these exercises give you the best shot at developing a stronger core.