what are you asking Joe
There is much more to the "core" than what people are posting on here. The "core" consists of many muscles besides what was mentioned on here, one of the main one's is the transverse and also in my opinion, the PSOAS, which has a direct correlation to low back weakness, pain and in some cases instability.

When you look at this diagram you can see where the psaos begins and ends, it actually starts at the "core" which includes lower lumbar and erector spinae. If the psoas of any part of the core is weak, especially the transverse abdominus (the muscle that basically holds you erect) your transfer of power will be tough. Example of "transfer of power" would be a baseball player, tennis player, quarter back. Lets take the baseball player, when a player is at bat, and swings, the "tranfer of power" begins at the ankles, then transfers to the hips, tranfers to the core, where the rotation of power is, then to the upper region. The bat speed comes from the "core".
MUVIRSE mentioned that Squats and deads were enough, again dead wrong, because very little of those smaller muscles are not getting worked or activated.
Also, you have phasic and tonic muscles, on muscles and off muscles, in my training wether with the general public or working with athletes, when we work the lower body or doing hip-dominant exercises, I have them go through a series of muscle activation exercises to turn those muscles "on" so they will fire correctly........glute are a good example of being an "off" muscle until activated. Activating the muscles not will help it fire more effeciantly, it also aids in preventing injuries.