Brabham and Williams 1982 - Used water cooling of brakes - evidently there was enough water in the tanks for the whole season. This was dispersed early in race to reduce weight and topped up under FIA rules in parc ferme to make the minimum weight. Subsequently dQ'ed
Brabham 1980s - movable aero aids have been banned for sometime but a Brabham used a fan that was 'primarily for engine coolant cooling' but had the side effect of sucking air from under the car increasing downforce. Won a race before being outlawed.
Sierra Cosworth Turbo - mid 90s. During a Bathurst qualifying shoot-out, the pole winning car was inspected and officials discovered that a engine bay C02 extinguisher was plumbed into the intercooler (increasing efficiency and power). A rewrite of the rules was made overnight banning this in the race.
Sandown Enduro - early 90s. Allan Moffat needed to come in for a fuel stop (a splash and dash). The car made it's way into the pit lane when a crewman ran alongside the car with a fuel churn filling the car without a complete stop. Officials again reviewed the rules outlawing this practice immediately after a hearing found they had broken no rules.
Toyota WRC - late 90s. The team was banned for a year from world rallying after developing a part that bypassed the compulsory 34mm restrictor to limit engine power.
Kevin Bartlett - late 80s Camaro. Had every bolt drilled to reduce weight. When the car rolled during a race the car appeared to suffer huge damage - it was mainly due to the bolts snapping.
And from the world of sailing - I was in a race once in very light airs and a strong tidal flow in the harbor. After looking at the nav charts, observing the instruments and the shoreline we tossed the anchor off the front of the boat and began to edge into the lead. The wind was so light we had boatspeed less than the opposing current... so everyone was going backwards down the harbor.
The class rules required each boat to carry a standard anchor and length of chain (which are obviously very heavy). After a while, almost all of the fleet - we ended up leading with our anchor over the side - had followed suit. Apart from 4 boats who ended up about a mile downcurrent. When the wind picked up slightly and tide turned, these boats had remarkable progress and surged into the lead.
Something was fishy so we protested at the finish and upon inspection none of the boats had been carrying an anchor or a chain making them lighter than the rest of us and giving them an advantage in the light airs...