If your current core training programming is focused on developing a flat stomach and six-pack abs, the time you spend doing crunches and sit-ups may be futile. The shift in core training should be made for two reasons:
Training your core is about developing the muscles that keep your spine neutral and braced all day, not about flexing it repeatedly until the muscles fatigue while hopefully waiting for your stomach muscles to emerge.
Your time is better spent in the kitchen and grocery aisles than on your back doing endless sets of crunches. Most people will have core musculature, as we all need abdominal muscles to function. The trick is to keep your diet clean enough so that they will appear.
Once you've made the mental adjustment and realize that there is more to core training than aiming for a six-pack and subsequently leave this goal in the kitchen, it's time to re-assess your core exercises.
T-Nation published an article a few years back on Anti-Ab Training. The author pointed out that the core is used to keep the lumbar spine in place while we move and also helps to transfer force from our upper bodies to our lower bodies and vice-versa. In the article is a 10 Stage Progression of Complexity for core stability.
Anti-Ab refers to the idea that we should be training our core by keeping it immobile while adding resistance which serves the purpose of trying to either rotate, flex or extend the lumbar spine. Planking and anti-rotational (Paloff Press) exercises do exactly this.
Here are my three favourite Anti-Ab exercises:
Straight Arm Hanging Leg Raises.
Hanging from a pull-up bar, lift your legs up as high as they can, tilting your hips forward as you do so. Keep your knees and arms straight and brace your core as you lift your feet up towards the bar. The Front Lever is the advanced version of this.
Picture source: http://breakingmuscle.com/gymnastics/how-to-build-up-to-the-front-lever
Grab a pair of dumbbells and set-up in pushup position. With your feet apart, row one dumbbell at a tme towards your ribs as you anchor down with the other dumbbell. Keep your back straight and refrain from rotating as you pull up.
Picture source: http://www.crossfitignitesydney.com.au/crossfit-workouts/crossfit-workout-clean-and-renegade-row
Swiss Ball Pike
Start with your shins on a Swiss Ball, hands on the ground. Pull your hips up while keep your legs straight. Keep going until your back is perpendicular to the floor. The key will be to really brace your stomach muscles as you pull up.
Picture source: http://www.womenshealthmag.com/fitness/superset-1b-stability-ball-ab-pike