House Rule #1: No Mo' Yo-Yo

Over the years, we've all home-brewed our games across all the versions and systems to fix the little things we personally find problematic. Maybe it's to make the game a little grungier or perhaps more heroic. Maybe the house rule is only for a specific campaign as its inclusion contributes tonally to the game. Whatever the reason, house rules make the game more your own and teach a valuable lesson: Your Fun trumps The Rules as Written - so write your own!

Context for this house rule

Dungeons & Dragons has become less and less squishy with each new edition. 5e has Death Saves, a holding pattern where just 1hp of healing has you back in the fight. Getting back in the fight is more fun for anyone knocked out early, but it can sometimes get a little silly with characters yo-yoing between "OMG I'm gonna DIE!" to "Argh! Taste my cold steel!" back to "OMG I'm bleeding out AGAIN!" to "I'm back!"... you get the idea.

Hit points are, by design, an abstraction of health, vigour and have-all-my-limbs-attached that keep you perfectly capable at 1hp, no matter how many times you've been dropped this battle. This house rule addresses that.

No Mo' Yo-Yo (or 6 strikes you're out)

Summary
If you drop to 0hp…. You get a level of exhaustion when you revive.
In addition, for each failed death save… You get a level of exhaustion when you revive. These are cumulative to any exhaustion you already have and with each other.
Passing a death save means nothing in the context of this house rule.

Full explanation
When your character drops to 0hp, have that player record that they are owed +1 exhaustion level. Then, each time they fail a Death Save (up to two otherwise they're dead) have them add another exhaustion level for each failure recorded. 

When (or if) they are revived, have the player add the total exhaustion they've accrued (possible maximum of 3 new levels) to their character. These levels of exhaustion are added to any the character already has, which if it totals 6, may kill him outright.

Example:
Rojek the Fighter is in a deadly fracas against a brutish bugbear. The bugbear clobbers him for so much damage that Rojek drops to 0hp (The player quietly notes he is due a level of exhaustion when/if revived).  Over the next two turns he fails one Death Save and the bugbear clobbers him for an instant Death Save failure. Rojek's player adds 2 more levels of exhaustion to the first for dropping to 0hp and makes pleading eyes with the party's cleric, his new best friend. Clarence the Cleric steps in, casts Cure Light Wounds upon him and Rojek is revived, back in the fight with 4hp and 3 levels of exhaustion.  He staggers to his feet, this going to be a rough day. 

The bugbear then hits Rojek again and does enough damage to drop him again to 0hp (The player notes he must add yet another level of exhaustion when/if he's revived again... and as long as the bugbear doesn't hit him or he fails any death saves)... he's going to be on Level 4 exhaustion. 

Rojek's player is in a tough spot... does he want to risk be revived again... although if he stays there and lets the bugbear wail on him.