In Pathfinder, I usually allow my characters max hp until level 3. I feel it gives them a better edge.
And instead of rolling extra dice for criticals, we just roll normal damage, add in Strength, and double it.
We allow sleeping to fully heal you and restore your spells and abilities.
Other than that, we try to stick to the rules.
I stopped rolling for hp a long time ago. The higher your hit dice, the more penalized you are when you roll low.
I just have everyone take the average (round down at even levels, up at odds).
Same thing with ability scores. No more randomization. Point buy and standard arrays all the way.
Rolling dice to determine success or failure is fun. Rolling dice that influence every other roll you make with the character for the rest of the game is not.
"Yeah, I kept rolling until I got a set I liked."
--was this person openly admitting to cheating, or did they honestly think that this is acceptable?
I think he thought it was acceptable. When I talked with him privately, he said he "needed" the high ability scores...
That's awful. At least he left.
Sitting down to a long running campaign with a character that has sub-par ability scores--especially when other player's characters fared better at creation--sucks.
Players at my table pick any ability scores they want, there even and three odd, with the sum of all modifiers equalling +6. It doesn't punish min-maxed characters (the game itself will do that plenty), provides just the right level of power I'm looking for and is easy to explain to new players.