Just so we all know what we are talking about lets define your core.
Definition: The balanced development of the deep and superficial muscles that stabilize, align, and move the trunk of the body, especially the abdominals and muscles of the back.
Core training theory: the purpose of training "your core" is because somewhere along the line of evolution we became lazy, overweight sacks of adipose tissue and the deep muscles of the abdomen and muscles surrounding the spine no longer function as they were intended to. You core muscles are supposed to fire milliseconds before your body engages in any movement or aggressive exercise. This "firing" protects the spine by creating a tight supportive column of muscle that prepares you for aggressive movement.
So in todays perverse exercise culture the market gurus and psuedo trainers have you doing tons of stability ball crunches, weird bosu ball exercises, reverse crunches etc. Most of these are, if not a waste of time, at lease an inefficient means of getting a stronger torso and in the process losing some bodyfat. In the early days of this core focused training a lot of trainers starting training athletes with a focus on this. They put away the heavy squats, cleans and deadlifts and had these athletes "draw in the core" and balance on one leg while squatting on a bosu ball. What they created were a bunch of football players who couldn't effectively block and tackle or move an opposing player out the way. The upside of all this core training is these athletes sure looked cute when they got their belly buttons pierced and headed to the beach in a mankini. Total and utter hogwash, typical of most trainers out there.
What any good strength and conditioning coach always knew and what CrossFit has brought back into the light is the absolute necessity of functional movements. These are movements you do in everyday life. Squatting, picking things up, putting stuff over your head. The exercises that accomplish this best tend to be compound barbell type movements like the dead lift, back squat, overhead squat, cleans, snatches etc. Add to these if you will a steady does of kettlebell swings, pull ups, push ups and other gymnastic type exercises and now your training your core! You will now be a person who is " harder to kill and more useful in general". That last quote is my favorite from strength and conditioning coach Mark Rippitoe.
I know, we now have made you a core training super cyborg with all these old fashion moves but your still a little soft around the midsection right? Guess what? This has very little to do with the exercise selection and more to do with the fact that you like like to eat pizza, pasta and drink too many adult beverages. When you clean up your eating habits ( Paleo diet/zone diet) and train like an athlete versus a primadonna bikini model things will change for you. You will find yourself performing like an olympic gold medalist combined with a Navy Seal wrapped in a suit of body armour and looking better naked in no time at all.
For those of you who of you who are little more stubborn you can still find a good Pilates dvd or the abdomizer online. Good luck with that!
Eat for growth, train for strength, live for the MOMENT.