In terms of height and width, the new iPad 3 and iPad 2 are identical. The difference lays in its weight, thickness and a slightly redesigned tapering shell. Now given that the front display and bezel is identical to that of the iPad 2, you can expect screen protectors, covers and cases which just cover the front like smart covers or non rigid cases to be perfectly compatible.
In the same aspect, sleeves and other kinds of cases that give enough room for you to easily slip in the tablet should be compatible with the iPad 3. However if you happened to have one of those hardcover cases which are designed exactly for the iPad 2, then it will not work on the iPad 3 mainly due to the different tapering and extra thickness. We have new 360s, iShields and Hard Covers arriving in late March.
Bluetooth keyboards, chargers and cables will be compatible. Check out our selection for New iPad Cases.