Teaming with Frank Williams in the 1980's Formula One arena, they took both the Constructors' and Drivers' World Championships on multiple occasions, at one time taking both in the same year. The 1987 season saw Honda power take a 1-2-3-4 finish at the British Grand Prix, which set the stage for pushing Ford and its Cosworth series of V8 engines off of racing's most prestigious motorsports podium for keeps.
On an interesting note, Honda took a Formula One victory in a car featuring their own chassis and V12 engine in 1965, nearly two years before any American car and engine combination could claim the same.
Honda's performance in all levels of motorcycle racing (250cc, 500cc, 1000cc, SuperBike, the list goes on) can only be described as legendary.
The latest hit on American cars attempting to keep up has been at the Indianapolis 500. The 2006 running of this race saw Chevrolet giving up completely and not supporting one single team, fearing that Honda would completely thrash its Chevy V8 (an Ilmor 256 design). The 2006 race saw a perfect reliability record by all of the Honda-powered cars, with all race finishers being powered by Honda. Any DNF's were usually caused by driver error and crashing (with that Honda engine still running hard).
That cowardly decision by Chevrolet Racing to simply give up proved to be a huge PR failure for General Motors.
Race Fan: "Man, that Honda-powered Formula One car just blistered out a 1.7 second 0-60 time. A great example of Honda Racing making its mark."
Neck-boy: "My 2002 Chevy Camaro can do that!"
Race Fan: "Oh, really...by the way, where is your Chevy?"
Neck-boy: "Back at home. I'm all greasy from crawling under it every week because it breaks down all the time...but Chevy's rule! YEAH! Mine's a cherry with only 24,000 miles on it!"
Race Fan: "Sure. Only 24 thou'? Wow, it must break down a lot. Hey, you need a ride home in my Honda Civic? Granted it's a bone-stock 1993 with 287,000 miles on it with the original motor, but it still runs great."
Neck-boy: "Uh, no thanks. I'd rather walk the 7 miles to my house in this 106-degree heat and risk a heat stroke rather than be seen in your intelligently designed, financially-smart and incredibly reliable foreign car. Nothin' personal, but my friends would make fun of me...you know, peer pressure."
Race Fan: "Suit yourself. Hey, why is your Camaro a 2002? Can't you get a newer one?"
Neck-boy "No, GM quit producing them after the 2002 model year because nobody was buying them."