Possibly the most simple, yet effective, core in the game is the GWF core, which is simply the starter trio. It's not overly common, but I'd wager a fair few people on the site have used them before and I'm wondering what other people like to use as their core. Post a few trios if you like, and you can be as detailed as you like (from just names to full sets). My prefered GWF core is:
Breloom @ Choice Band
Ability: Technician
-> Rock Tomb
-> Spore (Wut? Spore on a banded set? Yeah, I know, it has a nice surprise though)
-> Mach Punch
-> Bullet Seed
Empoleon @ Choice Specs
Ability: Torrent
-> Ice Beam
-> Surf
-> Hydro Pump
-> Grass Knot
Chandelure @ Choice Scarf
Ability: Flash Fire
-> Shadow Ball
-> Overheat
-> Trick
-> HP Grass
Pretty simple, they cover each other's weaknesses for the most part (Chandelure covers Empoleons fighting weakness and Brelooms fire & bug Weaknesses, Empoleon covers Brelooms flying weakness and Chandelures Rock weakness, Breloom covers Ground for the other two, Rock for Chandelure & Electric for Empoleon) also, they form a pretty strong offensive core and not many people are prepared to face the horror of three choice users.