A number of mine have been mentioned, but to add/expound:
- College football OT. Just play it out instead of starting in FG range, which is the equivalent of starting a runner on 2nd in extra innings, imo. The NFL OT isn't ideal, but at least they play football and have certain requirements before declaring a winner... or a tie. Ties after extended play are not the end of the world, and at some point player safety due to fatigue needs to be considered. My conversation-starter for college is to play a 10 minute OT period. Either be up by 2 scores (i.e. 9 points) or more to end the game before the 10th extra minute, or end after the 10 minutes (70 total), win, lose, or draw.
- Fouling out in hoops. I don't follow the NBA, but they also follow the one foul per 8 minutes rate (5 over 40 in college, 6 over 48 in NBA). Why have players foul out at all, and especially when in OT? In OT, at least grant each player one extra foul, but I would rather see a player have a mandatory 'penalty box' time after a foul ala hockey, than to foul out of the game completely. 2 minutes is fine. Maybe after 5 fouls, a foul is a 5 minute penalty. Follow that through the entire 40 minutes, and the whack-a-mole fouling at the end of a game would slow down considerably.
- College football kickoffs and fair catches.... If a player calls for and catches a kickoff in the field of play, spot the ball at the 20 rather than the 25 (the entire rule is a pet peeve, but it is here to stay). Don't penalize the kicking team for, in some cases, strategic placement of the kick to help prevent a long return. The coffin corner kickoff is smart, and takes skill to pull off. End zone kickoffs placed at the 25.... not great, but ok. But then why not punts into the end zone, which still gets placed at the 20?
- Some people advocate for 4 10 minute quarters in men's college hoops. I could be ok with that, but I like the uniqueness of the 2x20. Before the rule changes in football due to safety issues, I used to think it would be great to have football broken into 3 20-minute periods ala hockey. There would be another end of 'half' 2 minute flurry on offense, an extra kickoff, which used to be an exciting play, and an extra rest and re-strategize period for the teams. Instead of a 20 minute half, make it 2 12 or 15 minute breaks. The 3rd period kickoff would be determined by another coin toss; the 2nd period kick would follow the existing rules. This is all moot, of course.