Okay for the record, only sports which could conceivably be super powers are ACTUAL REAL SPORTS. The rest are just flouncing around getting swag and scoring medals and free food and vacations.
Obviously running is a real sport, as Super Speed could be used to foil crime and catch ne'er-do-wells (and let's face it, that dude running the 400m with no legs clearly has super powers, no question). Jumping likewise is clearly a super power and would gain you admittance to the Super-Secret Justice Club League.
Boxing, wrestling, fencing. Man those are shoo-ins. Javelin, archery, discus and all shooting events likewise clearly have martial applications and while they wouldn't get you your own movie franchise, you could certainly be a part of someone else's team (or perhaps a trusty sidekick. "Quick, Wrastlin' Ricky, unlock these chains before Commodore Chaos returns!" boomed Justice Man). You'd be on the collectable cup that no one really wants or treasures, but hey, you're on the cup!
Trampoline? That gymnastics thing with the ribbon? Synchronised swimming? Sorry, these are clearly not super powers and cannot be used to fight for Justice (wherever the reek of evil is to be sniffed, there shall Ludmilla and her Trampoline of Justice be found). Sorry tennis, sorry kayaking (The bank has been robbed! Captain Kayak raised his fearsome eybrow. "Did the miscreant flee riverwards?"). Not a single equestrian event is a sport (Oh no, the League of Darkness have secured their HQ behind that fence made of red and white poles, who can help us now?). I will grudgingly grant swimming, as Aquaman and the SubMariner are clearly super heroes, but only just. Water polo and volleyball are out. One cannot fight the Legions of Doom with volleyball, or even with skimpy volleyball outfits. Cycling is a super power, I'm sure Bruce wayne has used a BatBicycle before now. Sailing is out.
All winter olympic events are out. Sliding downhill (and all the variants thereof) cannot hold back the Forces of Evil. Neither can figure skating, as no known villain has 'triple axle' as their secret weakness.
Table Tennis has no place in the battle for Liberty, as the dismal performance of the Ping-Pong Brigade against the Wehrmacht during World War Two amply demonstrated. But let's not forget that though their balls may have been crushed, that they died facing the enemy paddles in hand. Like men, dammit.
So enjoy the olympics my friends, and enjoy them well. And let the unjust tremble!