Only a Flesh Wound: Advantages of not being at full HP

Normal HP drops in the Binding of Isaac come in two distinct varieties: Half Hearts and Full Hearts, and it's essential to know the difference to make full use of your HP bar.

A number of items in the Binding of Isaac trigger specifically when you take damage that would reduce your total HP (not soul hearts) to 1/2 or less. Here's a quick list:

♥♥♥♥♥ of Babylon: This classic passive item will give you a hefty stat boost while you are at/below 1/2 heart.

Scapular: A holy aura that grants you a free soul heart when you reach 1/2 heart (once per room).

The Polaroid (trinket): Protects you with a temporary shield for about 3 seconds when you reach 1/2 of a heart.

Umbilical Cord (trinket): Spawns Lil' Steve to protect you when you reach 1/2 of a heart.

Of these, the Polaroid is notably the most common, appearing in nearly every game, and as such, making full use of it is always handy.

Specifically, this strategy applies mostly BELOW the Depths 2 - Using it before the Depths 2 is only a detriment to you, and additionally lowers your odds of running into a devil/angel room (for which full HP increases the odds), however, below this point, where all enemies do full heart damage, this strategy becomes more and more useful.

Why?

Well if you're always going to take full heart damage from everything, let's analyze two situations:
You have 5 HP - you take 4 hits, the 5th hit kills you.
Versus
You have 4-1/2 HP - you take 4 hits, the 5th hit kills you.

In both scenarios, you will die in an equal number of hits, but with ONE major exception. In the second scenario, the Polaroid and other 1/2 heart items will trigger, whereas with full HP they will NOT!

Of course, this opens up room for abuse: If you keep your HP intentionally at 1/2 of a heart at all times, and stock up on soul hearts, these abilities will trigger with EVERY hit (WoB will remain active permanently) and thus will maximize the utility of the polaroid. Imagine that, with every hit, you get 3 seconds of shielding. You'd last a lot longer with 3 seconds of invulnerability per heart than with a few more hearts to take hits!

That being said, while deeper in the game, you should make it a point to ALWAYS keep your HP with half a heart open at all times.

How can this be maintained?

Leave half hearts on the ground, do not collect them unless you have a full heart open, instead of a half (as in you have 1, 2, 3... HP, and not 1-1/2), leaving them lying around can help you return to 1/2-open status easily if you accidentally fill up.
ONLY collect full hearts until you are at 1/2-open status.

If you intend to maintain 1/2 heart only status, do not collect any soul hearts until you reach 1/2 heart, then backtrack and nab all of them, doing so will also mean you'll have to avoid picking up any normal hearts in the process.