This might be more of an anecdotal question, but are there any aircraft where under full throttle (with afterburner in worst-case) where the wheels wouldn't provide enough friction against the runway to keep the aircraft from starting to roll (and skidding the locked-up tires)? Obviously if the runway was iced it would make a difference in friction; I'm more wondering about in normal runway temperatures where it's just rubber on concrete.
Many small 4 to 6 seats propeller airplanes can overcome their brake/wheel holding capability, on concrete and ashpalt. My Cessna Cardinal is 180HP, I do engine pre-takeoff runup checks at 1700-1800 RPM. Going to 2600, the plane will start moving. Many other planes of similar size are 300 HP, and they definitely won't hold. We only have two 5" or 6" disc brakes, no power assist, pushing the pedal tops with our toes. Or a hand-pull parking brake.
Many aircraft can overwhelm their brakes from engine thrust. In the bad old days there were a handful of planes which went down because they taxied with their brakes fully on due to a danger of fire in throttled down engines or because of weather conditions. This in turn heated the brakes to the point that the hydraulic fluid burned and the plane went down shortly after takeoff. The loss of Swissair 306 prompted the use of non-flammable hydraulic fluid after that point.
The above incidents of brakes failing because of overuse of the brakes to restrain the engine might not really be what you mean. In terms of the engines of an aircraft to overwhelm the braking capacity immediately after spoolup, many fighter planes post WWII could do this. Generally the tires would skid forward without the brake rotors spinning inside the pads. Consider an F-15, one of the first fighter planes to have a power/weight ratio greater than 1. This means that in the right configuration the plane could overcome an extreme amount of friction between tire and runway since the engines could produce more lateral thrust than the entire weight of the plane pushing into the ground. Most fourth generation fighters could produce P/W greater than 1 at 50% load and nearly all could do so at minimum load.