In fact there were three. Boxing and wrestling are well known to this day, but they were child's play compared to the pankration.
I don't suggest you try playing this at home kids, but here are the complete rules for a pankration contest:
1. No biting.
2. No gouging eyes.
3. You can surrender by raising your arm.
4. If you're unconscious or dead, you lose.
Notice there are no rules against breaking bones, grabbing and twisting where it hurts most, or using choke holds. Two referees circled the contestants with sticks or short whips and beat anyone who broke even these simple rules. In the picture you can see the referees to the outside, one wielding a whip; the contestant on the ground has raised his arm in defeat.
There is a modern martial art movement which calls itself pankration, but needless to say they don't fight according to the ancient rules. It would be grossly illegal!
Choke holds seem to have been a popular way of winning, hence the rule that if someone loses consciousness or dies then it's game over. I'm not kidding about the death part. People regularly died at Olympic level. So regularly that contestants were issued a blanket pardon for murder before the Games began.
One man called Arrhachion won the pankration at three Olympiads in succession! This means Arrhachion was not someone you would wish to annoy. Arrhachion in an important way embodied a Greek ideal which is largely lost to modern society, though some people still naturally retain it, and this is the importance above all else of achieving excellence. Not the pursuit of excellence, but excellence. There are athletes and academics today who, if they come second in a contest, turn around and say, "I lost." Any Classical Greek would have understood that and agreed wholeheartedly. At the ancient Olympics the only prize was for coming first; none of this bronze and silver rubbish. Likewise there was a first prize in choral and dramatic contests and that was it.
Here is how Arrhachion won his third Olympic crown. Keep in mind as you read this, Arrhachion knew what he was doing, and could have raised his arm at any time. We take up the fight with our hero in big trouble:
Arrhachion’s opponent, having already a grip around his waist, thought to kill him and put an arm around his neck to choke off his breath. At the same time he slipped his legs through Arrhachion’s groin and wound his feet inside Arrhachion’s knees, pulling back until the sleep of death began to creep over Arrhachion’s senses.
But Arrhachion was not done yet, for as his opponent began to relax the pressure of his legs, Arrhachion kicked away his own right foot and fell heavily to the left, holding his opponent at the groin with his left knee still holding his opponent’s foot firmly. So violent was the fall that the opponent’s left ankle was wrenched from his socket. The man strangling Arrhachion … signaled with his hand that he gave up.
Thus Arrhachion became a three-time Olympic victor at the moment of his death. His corpse … received the victory crown.