Game-Breaker: Actual teamwork. Coordination can result in the enemy team being completely disabled and held back. A few knights protecting decent archers can slaughter the enemy team with a hail of arrows while no one gets remotely close to them.
The overhead-look down exploit. Take a weapon like the Maul or Zweihander - extremely slow weapons that are capable of One-Hit Kill attacks, then run around staring at the ground while using the overhead attack. The animation tends to play after the attack, resulting in an effectively unblockable attack that will drain almost all of a player's stamina.
Recently fixed, though the zweihander is still a bit subtle.
The infamous backwards overhead hit similar to the above-mentioned look down, but instead of looking down, you look directly away from your enemy and up at the sky, angling the overhead just right for an unblockable attack. Especially annoying given how ridiculous it looks.
Seasonal Rot: Many fans believe exploits such as the overhead tricks described above broke the game's realism, favoring cheap tricks over actual skill. A small group of fans even gathered together to make a Spiritual Successor, Mordhau, basically a remake but with the exploits removed.