One famous one has to be the german national team in the 1954 FiFA World Cup. They won against a heavy favoured hungarian team that had already beaten them 8-3 in groups.

Many belief that the main reason Germany was able to pull that upset were their boots. On the day of the final it rained heavily which usually meant for the teams to switch their boots but adidas had developed a boot where you could simply switch the studs acccording to the conditions, giving them the advatage to play in their normal boots.

(http://en.wikipedia.org/wiki/1954_FIFA_World_Cup_Final, http://www.herzogspark.de/media/cb1fdde7-8a1b-4dc9-a86e-62d9fee49aa9/Adi-Dassler-Ausstellung-WM-1954.pdf second source is german srry)

The German Democratic Republic was so succesful in Sports because of their high investments in sports education and research. Regarding research there is a very succesful institute still working for Germany because it was so succesful. And many of Germanys olympic medals are based on achievments of that institute. http://www.fes-sport.de/ This govermental socialist institute invented carbon frames for bicycles and shocked everyone else and they are still producing the carbon bikes for german bicycle teams. They were and are one of the major inovators in sports. http://www.fes-sport.de/ http://de.wikipedia.org/wiki/Institut_f%C3%BCr_Forschung_und_Entwicklung_von_Sportger%C3%

I am also not a historian, but this question is very intriguing to me, so I did a bit of searching.

The results I've found have said a lot about J.W. Foster's spiked-sole running pumps, which apparently did not include rubber, but did provide traction to runners using one-inch spikes on the bottom of the shoe. (This source says that a version of the shoe with flat, rubber soles was also made.) Other pages I read regarding these shoes are here and here. According to these pages- and I can't say how reliable they are!- runners using these shoes broke multiple records.

However, I have not seen anything about controversy. As /u/jackamoxc noted, runners who saw that the shoes improved other athletes' performance were probably quick to get a pair for themselves. The only information I could find about the reaction to the shoes' use is that their popularity spread quickly by word-of-mouth when athletes such as Alfie Shrubb broke records while wearing them, and by letters from runners to J.W. Foster's shoe company that praised the shoes- these letters were published by Foster to advertise the shoes.

Also interesting are the Dassler Brothers' spiked running shoes shown in this article. Again, there is no mention of a reaction from the public or from other athletes.

I hope this serves as a good starting point for more research, since I couldn't adequately answer the question.

The 1989 Tour De France. This was a time before doping in a serious way, any performance enhancing drugs could be caught in tests and most drug use was recreational. Lauren Fignon, a phenomenal cyclist in his day was on course to win a third Tour De France. His closest rival was Greg Le Mond and Fignon felt he had done enough during the race to get a comfortable lead. The last stage was to be an individual time trial which Le Mond would be better at, but fignon felt he had done enough...then out rolls LeMond on areobars, allowing him a significant advantage in terms of aerodynamics. Le Mond blew everyone away, and went on to win by 8 seconds, the closest margin in tour de France history.

Fignon was very angry and bitter. Aerobars were banned by the tour but the organisers did nothing to enfore these rules. Cycling rules can be a bit unfairly and selectively enforced. Fignon himself showed up at a different race with them and was refused to be allowed start if he used them!

Since then they have become commonplace.

Fignon spent the rest of his life correcting people "no, I am not the man who lost the tour by 8 seconds, I am the man who won it twice"

Today the rules about the bike are better enforced. The bike is limited by the rules a lot, such as minimum weight well above what modern materials could safely produce, limits to shape of spoke, and limits to shape of aerobars.

Everynow and then there are allegations of mechanical cheating, such as putting ice in the frame so it weighs ok at check in, but the ice melts and the water drains making the bike lighter than allowed. To combat this they have spot check weigh ins after too.

There was also once an allegations that someone had a built in engine in thier bike, so now bike are X rayed at the end of a days race, even though this was never more than a silly rumor.

This article has some interesting related info, although it focuses on the arrival of the slap skate in speed skating it is a similar situation where an invention in material dramatically changed a sport including calls by at least one big name to outlaw the new skates and reluctance by many to switch over until the dramatic effect on results was shown.

I know it falls inside the 20 year rule so feel free to delete it but I think it's worth mentioning.