Both slotted rotors and cross-drilled rotors are designed to dissipate the vaporized gases which form between the brake pad and disc itself during hard braking. This eliminates brake fade and greatly improves brake cooling in two ways: more channels which allow surrounding air currents to flow through the rotor, and by simply having the disc made out of less material.
Rotors which are only slotted are, in my opinion, the strongest as they lack thru-holes which can crack in the heating and cooling cycles of everyday driving.
Rotors with drilled holes can, as previously posted, crack around the outer diameters of the drilled holes, compromising strength. Some extremely cheap after-market rotors also lack chamfers on the holes, thus destroying brake pads in very short order.
Cross-drilled and slotted rotors look awesome, but wouldn't be my first choice for a daily driver.