Most (with one exception that I know of) require at least an 18" wheel with the appropriate offset in order to clear larger calipers/rotors.
In addition, larger brakes do not stop your car any faster. Tires stop your car. If the stock brakes can lock-up the wheels (or cause the ABS to activate) at 20 mph they will do so at 200 mph. Larger brakes will however be able to absorb more heat. Larger calipers have greater fluid volume and larger rotors make a better heatsink. More pistons help to prevent pad taper as well.
The real secret is to get cooling air to the brakes be they stock or otherwise. The stock brakes can be improved with the addition of cooling ducts, better fluid, SS lines, SS or titanium/vented caliper pistons, and pads appropriate for the intended use (street or track) no single pad will excel at both.
I saw a Z06 with Wilwood 6 piston calipers and larger rotors and he ended up having to go to a larger master cylinder as well in order to regain adequate pedal modulation. Initially the brakes would go into ABS with the mere touch of his toe.
They did fit under the stock wheels though.
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