I think the core can be strengthen by 2 main "methods":
1. as a by-product of heavy compound exercises like Squats (especially Front Squats) & Deadlifts, as well as other leg exercise like Split Squats. Overhead Pressing works well if the tempo is high (30X0 or more say). Overhead Squats are also useful, but many people cannot do these. Even press-ups help strengthen the core, especially if weighted.
2. direct core/ab work. So, choosing exercises that actually work the core as their main goal. Standard ab crunches etc work the abs, but the core is a lot more than just the 6-pack. So, exercises like the plank (for the relatively weak core individual), to exercises like DB Pull-Ins, DB Press-Up & Twist, Pallof Presses and other cable exercises that require the body to resist twisting.
Does that answer your question KP?
EDIT: T-Nation have an article out today about the core:
http://www.tmuscle.com/free_online_arti ... gger_liftsSome good stuff in there.