A fairly common adage among Magic: The Gathering players is that, while you start with 20 life points, only the last point really matters. Cards like Channel (allows the player to exchange one life point for one point of mana to cast spells) and Necropotence / Yawgmoth's Bargain (pay one life point to draw one card) turned out to be brutally overpowered as designers did not immediately anticipate that players would gladly pay all their life but that last crucial point. Turns out it's pretty hard to lose a game where you've just drawn 19 extra cards.
A corollary to this is that cards that do nothing but give you life points are considered worthless, except in very exceptional situations.
It is potentially possible to put together a deck which abuses life-gain cards and uses cards which get better when you're above a certain life total...
Interestingly, this was averted in earlier editions of the game; a player didn't lose, even with no life points, unless a phase ended. Prosp-Bloom, the first combo deck, exploited this by playing cards like Vampiric Tutor and Infernal Contract, often dropping to a negative life total in the process of assembling the combo, before finally casting a mammoth Drain Life that would both kill the opponent and gain enough life to get back to a positive number. In fact, the entire point of the Mirror Universe combo deck was this.
Since the Yu-Gi-Oh! trading card game was directly inspired by Magic: The Gathering, this trope applies just as much to it. You're still in the game as long as you have Life Points left, and it can sometimes be to your advantage to simply take a hit and sacrifice some LP rather than waste a vital card on a stopgap solution. A number of powerful effects, including the all-negating Solemn Judgment and the summon-negating Solemn Warning, demand a high cost in terms of LP, but if that 2000-4000 LP thwarts the opponent's game-winning move and gives you a chance to retaliate, it's an investment well spent.
And now there's Endless Decay, a horrifying monster which has its ATK equal to half your opponent's Life Points. It becomes even easier to summon the few turns between you and Critical Existence Failure.
In the Naruto and Dragon BallTrading Card Game, injured status has its own separate point values. They are often weaker, sometimes stronger, and sometimes they stay the same.