Not many likely bothered with it much, but in some of the classic 16-bit Sonic games (this old man's memory is letting him down and he can't remember which ones) you could play against a buddy in splitscreen. It was a fun idea, albeit the framerate would dive; granted, in those days not many of us minded shoddy performance as much as we do in modern gaming.
In any case, in the name of nostalgia there'll be a Competition Mode in Sonic Mania. The winner in each round is determined by completion time, the number of rings collected and more.
Sonic, Tails, and Knuckles are all playable characters in Sonic Mania’s Competition Mode. Winners are determined by a few factors: clear time, score, number of items acquired, number of rings acquired when clearing the level, and total number of rings acquired throughout the level. Players can adjust the rules of each match by adjusting items in the item boxes and number of rounds that take place.
It looks rather fun, and is yet another nice additional mode for a title that has us full of optimism. Sonic Mania is out on 15th August, so there's not long to wait now.