Most of these I came up with while running a successful year-long campaign:
Instead of rolling damage dice, I just use the average value listed in the Monster Manual. This has a few benefits: it’s faster, still within the rules and players don’t usually care at all. Critical hit? Use average damage plus a die roll. Or just double that average damage value.
Adjusting Monster HP
To make a monster easier to kill (eg: to make a band of mooks, portray a wounded or weakened foe, to speed up a lagging encounter or to lower the difficulty setting if the PCs are having lots of bad luck), give the monster its minimum possible HP. To make a tougher monster, go maximum (or close to it).
Diversify monsters by re-skinning
Use the stats of something simulating the effects that you like and change the descriptions. Change fire breath to death ray or cold resistance to poison resistance. I’ve re-skinned a giant aquatic psychic sea monster into a sentient evil tree and no one noticed.
Players reward Inspiration
Takes some extra work away from the GM who usually has enough to worry about already. Also, the GM gets to avoid giving the appearance of playing “favorites”.
Critical hit damage
Try this: apply maximum damage of that weapon plus another dice roll. So, for example, a short sword would deal 6 + d6 damage (not counting ability score bonuses). Makes each critical hit feel rewarding.
Player fails a skill check. Let them take a level of exhaustion to get a solid pass to represent tremendous effort or strain.
Featured image: Pillars of Pentegram by Larry Elmore