8x8 Matrix LED problem

The schematic you posted is for common cathode (i.e. ROW = CATHODE) displays. If you use a common anode (i.e. ROW = ANODE) display you have to switch the connections (13 <-> 9, 3 <-> 14,...). See the attached image. And as Matt wrote, you really should use resistors to limit the current (R = 470 Ohms should be OK).

CommonAnode.gif