Overview

Here are a few adjustments to rules that may make your experience better. These are established as optional rules for D&D 5E, but could be used for other TTRPG with some conversions.

Death & Dying 

In D&D 5E the fear of death continues to dwindle as you gain higher levels. It has gotten to the point were death has become completely reversable just by having enough gold. If you wish to make players care more about what choices they actually make, try implementing some of these to really give death a meaning.

Limited Return

As long as you have the spells or gold, there is no limit to how many times you can return from the dead. With this, it puts a cap on how many times a soul can be returned from the dead. Showcasing the difficulty for a soul to continue existing in the world.
You soul can only return to this world a number of times equal to 1 + your Constitution Modifier. Once it has reached its limit, it can never return.

Worn Body

A difficulty with how the current state of falling to 0 Hit Points means there is no reprecussions. A simple healing spell will get you right back up like nothing happened. Falling back down and getting up repeatedly is know as "boomeranging" and can feel like dropping to 0 has no real meaning.
When you drop to 0 or below Hit Points, you gain one level of Exhaustion.

Looming Death

A real concern is how magic seems to fix too much an really doesn't give you a consistant fear of dying. When you fail a Death Saving, it might feel as though you have something to worry about, but with a simple healing spell all of them get reset. Make your players feel like repeated combat can be actually dangerous.
You can only reduce your Death Saves by 1 when you finish a long rest. This means if you have 3 Death Saves already, you will die the next time you fall to 0. 

Value of Life

A big problem is how cheap it is to return someone from the dead. Within a minute it cost less then a magic item. Even for some of the higher tier spells it can cast less then a rare item. I use these terms of items rather then gold, because even if your DM doesn't hand out a lot of gold to try to fix this problem, you can just sell off magic items you find to fund this cost. There are two different ways you can fix this problem.
Add a 0 to all component costs for diamonds. A simple Revivify requires a 300gp diamond. This would change it to o3,000 gold and make players worry about the cost of death.
Require a special item in addition to the diamond that would be consumed. Diamonds are universal across all lands and can be easily found in jewelry and gem shops. Create a special revival item that is difficult to obtain that gets consumed when the spell is cast.

Death by Damage 

When you fall below 0 hit points you generally have a 55% chance at succeeding on that save. With 5% of that letting you instantly get up and act like nothing happened. Try using this rule to make the determing weapon a factor on how difficult it becomes.
When you are dropped to below 0 hit points and roll Death Saves, the DC increases by an amount equal to half of the triggering die that was rolled. Example: Dagger (d4) would increase it by 2, Fireball Spell (d6) would increase it by 3, Longbow (d8) would increase it by 4, Inflict Wounds (d10) would increase it by 5 and a Battleaxe (d12) would increase it by 6.   

Sneak Attack

This may sound familar to you as it is what the Rogue Class has or at least what it says it has. Sneak Attack isn't really a Sneak Attack based on how it is worded. A more proper name for it would be Advantageous Strike as Advantage and Disadvantage play a core role in it. Why is only a Rogue allowed to secretly sneak up on someone and strike them for additional damage. Trade in the Rogue Sneak Attack and call it Advantageous Strike and allow your stealthy party to actually do something with their sneaking.
When you hit a creature that is Surprised, you deal an additional amount of damage equal to 1d4 + your proficiency bonus.

Unconscious Attacks

Even when someone is at 0 hit points or asleep, it still requires an attack roll. This can really irritate players to no end when someone in this state "dodges" an attack. Even a creature in full platemail has easy to acess vulnarable areas.
As an Action, deal your weapon damage to an unconscious creature. If an ability would trigger due to Advantage and that creature has Advantage. Trigger that effect.

Poisons

These can be some of the most versatile things in a game, but with a simple wave of the hand, it can be just removed without issue. Because of this, Poisons hae been severly tamed down and are one of the least used things in D&D 5E. The costs are high, the damage is low and the saves are easy to pass. Use these optional rules to help bring back the fun and flavor of these mechanics.

Strain Variety

A difficult thing is that no matter the type, application or potency, any poison can be wiped away with a simple catch all spell or ability. Either of these options can help with it depending on how much work you wish to put into it.
When a spell or ability that is used to remove a poison, a Nature check is required to identify the type of poison and how to properly remove it. A creature trained in Poisoner's Kit has Advantage on this roll. On a failure, you do not know how to remove it and the spell or ability fails.
You could deem that these types of spells and abilities only cover basic poisons up to a certain damage level. This would require creatures to learn modfied spells and abilities to account for these different varieties of poisons.

Potent Poisons

Poisons can have a very low damage and low saving throw threshold to beat. This compiled with their high costs will dissuade anyone from buying them, let alone making them. 
Allow players to spend extra gold when purchasing poisons to increase their damage and save DC.
When a Poisoner crafts a poison, allow them to add their proficiency bonus to the preexisting save DC or use their own of 8 + proficiency bonus + Intelligence Modifier.