Off the top of my head:

Changes fall into two categories:

1. Rule Tweaks
2. New mini-systems.

Under 1:

• Shove is not a part of the attack action. It is a bonus action available to all characters. Shove only pushes the target back an amount that depends on the shover's strength and the target's weight. It normally does not knock them prone unless they are shoved off a high ledge.
• Weapons are given unique weapon action attacks depending on the weapon type. These can be used once per short rest only if the wielder is proficient with the weapon.
• Removed the requirement that attacks must be made using Strength to activate the benefits of Rage.
• Removed the requirement that attacks must be made using Strength to activate the benefits of Reckless Attack.
• Fast Hands simply gives you an additional Bonus Action with no restrictions.
• Haste simple gives you an additional Action with no restrictions
• Consuming a potion is only a bonus action.
• If a creature throws a healing potion as an action, it will break and heal all targets in a small radius.

Under 2:

Numerous weapons and items have systems attached to them that create or consumes various "charges" to add additional effects

As an example, weapons and items with the "spark" ability builds Lightning Charges in the wielder when certain criteria are fulfilled.

If 5 Lightning Charges are built up, the next instance of damage done with an attack role inflicts an additional 1d8 Lightning Damage.

There are many more. See Here and Here

People on the same turn sharing initiative can go at the same time. Drinking a potion is a bonus action. Those are the ones I've incorporated.

There are quite a few, but a simple one that I've put into my own house rules is giving all Clerics proficiency with flails and morningstars.