Most people are completely confused about what effective core training really is. The popular way of looking at core training is to eliminate crunches, perform a ton of unstable training and rarely use any movement that isn't a chop or a plank. This very misguided advice can actually limit and prevent you from getting a hard core.
1) You must include one heavy crunch movement. Crunches have gotten a bad name recently with new research showing increased spinal loads during the crunch but that doesn't mean there isn't a way to effectively perform them. The most effective and efficient way to perform crunches is on a swiss ball. You can limit your amount of spinal flexion(crunching all the way up) by working through a shorter range of motion.
I love the swiss ball as a core exercise for a hard core simply because it forces you to brace, stabilize and perform the movement. Adding some extra weight with a dumbbell, plate or swiss ball will help as well.
2) You must include one twisting movement.
Chops are popular for a variety of reasons but for a hard core, they are a must. Since they work the obliques like nothing else,you'll be forced to brace your core and resist being pulled back by the cable. This bracing movement further increases the activation of your various core muscles making chops a perfect core exercise.
3) You must include one reverse crunch movement.
These are probably the least popular of core exercises to perform because people don't feel them as much as the basic crunch. Being essential to getting a hard core, we have to do them. Decline board, on the floor or on the swiss ball are all good places to begin. Just make sure you flatten you abs and start the movement with your hips.
An effective exercise for a hard core would look like the following
Swiss Ball Dumbbell Crunches 3 sets of 8 reps
Low To High Cable Chops 3 sets of 12 reps
High To Low Cable Chops 3 sets of 12 reps
Decline Reverse Crunches 3 sets of 12 reps
That's just a sample of the hard core exercises that you get when you grab The Physique Formula and the special bonus ab program, The Crazy Cuts Manual.