The AFL (Australian Football League ) has a variation of the 8, but require some ranking.
1-4 is a group, 5-8 is another. 5 vs 8 6 vs 7, winner moves on loser goes home
1 vs 4, 2 vs 3, winners get a bye losers' play the winners of the 5-8 group. Single elimination from then on, and the brackets are set up so that teams in the 1-4 group CAN play each other again in the last game. And that has happened at least twice that I know of.