These are the only house rules from my games I've bothered to codify, with footnotes no less:
To determine their place in the initiative order, every participant makes either a Dexterity check or an Intelligence check. (1)
Inspiration may be expended to either gain advantage or to re-roll an unsuccessful attack roll, saving throw, or ability check. (2)
Hunter and beast master rangers gain a thematically appropriate spell known of their highest spell slot at 3rd, 5th, 9th, 13th, and 17th level from any class’s spell list. (3)
When you engage in two-weapon fighting, the additional attack does not use your bonus action but cannot be used on the same turn as another ability that grants attacks with a bonus action. (4)
A player can choose Intelligence instead of Charisma as the ability score that modifies their character’s warlock features, such as spell save DCs, spell attacks, and eldritch invocations. (5)
WEAPONS, SPELLS, AND DAMAGE TYPES
Existing weapons can be re-skinned as different armaments. For example, the properties and damage dice of a rapier could be re-skinned as a light thrusting spear. Feel free to change damage types as needed. Similarly, a player may opt to alter the type of damage dealt by a spell or ability when it is gained with the GM’s assent. Be careful with the force and psychic damage types; few enemies have resistance to those types of damage. (6)
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(1) - Intelligence is the least utilized stat in 5e; this house rule gives a tiny additional incentive to not dump it.
(2) - I've found that if you just let inspiration grant advantage, as per the rules as written, no one ever uses it because no one wants to gamble on a limited resource that they might not need to use. Having it offer a re-roll gives a greater chance that it will actually get used in play.
(3) - Rangers should have gotten additional spells known in-line with other half-caster classes. It looks like WotC realized that error, as all of the newer ranger subclasses give additional spells known. I could make a codified list of what those spells should be for the hunter and beast master, but I'm lazy and also fine with letting players pick the spells that fit their idea of what their character is all about.
(4) - This is a revision of the rules I proposed (and tested) here. It turns out that you don't really want two-weapon fighting adding on top of the monk's bonus attacks, as an astute commentator pointed out at the time. They were right.
(5) - This one has seen extensive playtesting in one of my campaigns and it worked just fine.
(6) - This one has also been playtested a lot in my games. It builds off this post.