American football:

Universal:

1. No TV timeouts. The game is already insanely stop-start. Get your shit together, TV broadcasters, and make it work as-is.
2. No "wounded duck" pass interference penalties on poorly thrown balls. Defenders in pass coverage should be entitled to their existing vector of motion.
3. Players leaving for injury must be out for 4 plays or more, maybe the length of the existing drive. Something though. One play is not sufficient to dissuade simulation for tactical advantage.

Stuff to try in college or the spring league:

1. No radio communication. American football can be too regimented sometimes, and old men treating young men like chess pieces is part of that.
2. Limited substitutions per play if there is no is no change in phase. You come out, fine, but you're not going back in until the next time your team is on offense/defense/special teams. This will also enhance numbers 1 and 3.
3. Even shorter play clock. Keep it moving. Adjust when the clock runs if you want to keep the number of snaps consistent.
4. Remove kicking entirely. They're vestigial minigames at this point that could be replaced with throwing the ball. Workshop it in the offseason to see how small the goalposts need to be to replicate current play balance.
5. College only: Admit they're professionals, make them employees with enforceable (and purchasable) contracts, and route enough money into the non-revenue sports to keep them viable. It is what it is; don't let the creeping in of sensible labor practices destroy the sport. Use the inevitable anti-trust exemption you'll get to mandate some sort of nexus between the players and the schools (lifetime tuition waiver? part-time enrollment?), but stop acting like the already snobbish and laughable "amateurism" of the NCAA is even a viable concept.

Stuff to bring in that would make the game weird to modern eyes but might help reduce head injuries:

1. Mandate wide splits on the lines, two-point stances, and a wider neutral zone so that players are not exploding into each other head-to-head. A snap should look like a sumo match, not two horny rams on a hillside.
2. To allow for number 1, make "1 yard to go" the minimum for a given offensive snap.
3. Remove most/all of kicking again, though with the idea of reducing high combined-velocity impacts rather than just because it's anachronistic. Treat an incomplete pass on fourth down like it was a punt. Give up on the idea of kickoff returns. Field goals could stay, but subject to the same scrimmage rules as other plays.
4. Consider whether every play from scrimmage should require the Offensive Line's first step should be backwards or lateral. They already are on many passing plays, but making it mandatory would further encourage upright play that's often ineffective technique today. The running game will be severely affected, but it is what it is and "every run play looks like a draw play" is a small price if we want to save American football over the long term.
5. Revamp tackling rules. Make it rugby style and penalize hits above the shoulder harshly. Consider whether big hits resulting in heads thumping against turf are common enough to be banned altogether.
6. Consider removing helmets so players have a sense of preservation over their own heads, but if not that, then go with something much lighter and more ice-hockey style so the helmet is not as tempting as a weapon and doesn't encourage a false sense of invulnerability. It was for all the wrong reasons, but the "Extreme Football League" (nee "Lingerie Football League") uses this type of headgear.