Okay, using the main site, here's a list of all of the renamed types, using the most common word in moves of that type as the new name. New types are first, and the old types are second.
Hyper - Normal
Fire - Fire
Leaf - Grass
Water - Water
Thunder - Electric
Order/Bug - Bug
Sky/Air/Peck/Attack - Flying
Punch - Fighting
Poison - Poison
Ice - Ice
Mud - Ground
Rock - Rock
Power - Psychic
Shadow - Ghost
Metal/Iron - Steel
Night/Dark - Dark
Dragon - Dragon
Remember, kids, Night type beats Shadow type, but both are strong against Power type. Power type is good against Punch type, which is in turn good against Hyper type. Attack type beats Order type, and Mud type is advantageous versus Thunder type (though it is weak against Leaf type).