If you want a strong, defined and functional core you must do two things. First, clean up your diet. Inflammatory foods such as gluten (and most grains) and dairy create inflammation in the gut which inhibits core function. But the second way to get a strong core might surprise some of you: stop doing crunches.
A traditional ab crunch is a flexion exercise. But the core wasn't designed for flexion -- its main function in any and every sport is to keep you from going into extension and rotation. Therefore, anti-extension and anti-rotation movements are some of the best ways to get a strong core.
Additionally, as many of you have probably felt for yourself, crunches can put excessive stress on your low back. According to Dr. Stuart McGill, professor of Spine Biomechanics at the University of Waterloo, a traditional crunch places 3,350 newtons (the equivalent of 340 KG) of compressive force on the spine. That much force can compress a disc's nucleus to the point where it bulges, pressing on nerves and creating back pain. Instead of crunches, McGill suggests exercises that strengthen the core while keeping the spine in a neutral position.
The Stability Ball Roll Out is one of my favorite exercises for doing just that.
To start, get into a tall kneeling position with your glutes and anterior core muscles engaged and your forearms on a stability ball. Slowly let the ball roll out in front of you, moving your upper body and hips at the same pace. As the ball moves, make sure there is no movement in your spine. The two most common compensations I see for this exercise are excessive arching of the low back and excessive rounding of the mid-back. Your goal is to maintain a neutral spine, so only let the ball go out as far as you can while controlling your posture.
In terms of sets and reps, you want to get into more of an endurance phase with core exercises. Whether or not you play a sport, you need your core muscles to be engaged and helping you maintain good posture throughout the day. So train them accordingly! Start with 3 sets of 10 reps and work your way up to 20 reps.
If you want to start easier, use a bigger stability ball and progress to using a smaller ball over time.