Mutants and Masterminds
Mutants and Masterminds is a D20(ish) system published by Green Ronin. Unlike a lot of other d20 games, this one only uses twenty-sided dice. Players make their own superheroes (or supervillains; there's no alignment in this game) and slug it out with each other or NPC characters.
The game revolves around power levels (M&M's version of character levels or challenge ratings). The standard PL for a player character is 10; this is about the equivalent of a normal comic-book superhero. PL 5 characters are more "street-level", PL 15 characters are more akin to Superman or other heavyweights. Power levels don't necessarily correspond to actual superpowers - a PL 10 Batman-type character could have a lot of gadgets and other "realistic" skills that puts her on the same level as someone who can fly unaided and shoot rocket dongs from his hands. Every Power Level grants 15 Power Points, which form both the character creation points and your experience points. The points you earn at the end of a session are used to upgrade your powers, and unless you have some really potent stuff you can upgrade something at least once every session. It's also a good measurement of your Power Level as you improve, since every 15 additional points kicks you up one Power Level. Power Level also limits how high certain things can be leveled: your Abilities, your Skill Modifier (Ability + Skill Rank + Advantages) are limited to PL+10, and the sums of Toughness and Dodge, Toughness and Parry and Fortitude and Will cannot be more than twice the PL.
There aren't any hit points in M&M; all attacks are either rated as lethal or not. When you get hit, you roll to see how much it affects you, and depending on what hit you, you either get stunned, knocked out or killed. You can also get knocked away some 27000 ft. by a fucking Hulk rip-off drug addict and spend special Hero Points to get up video game style, which are then replaced when you do a very heroic thing (such as stabpunching clear across a hockey stadium some fucking Kraven rip-off who just shot you).
Aside from skill ranks and feats, characters can spend points on various powers. M&M appears to have a rather narrow list of powers at first, until you realize that the list in the book is not powers, but rather effects. The game does not dicern between a regular punch, a fire punch, hitting someone with a tree or a hammer: all are attacks made at close range and can knock people out. Powers can be customized even more by adding extra modifiers or flaws: a teleportation effect might be able to carry passengers or move around without a BAMF effect, or an energy blast might not affect things that are yellow and/or made out of wood.
This system has been both praised for its flexibility and criticized as it can often lead to mechanically overpowered or simply bizarre characters. For example, with a cheap increase of +1 per rank and a limit on potential damage, the basic ranged attack power can never miss and has a range of, literally, as far as the eye can see. Never miss. Ever. As long as the character can see their target, the target is automatically hit. The system does however have many hard counters to abilities: being able to shoot anyone you can see matters very little when you fight in the dark or against a guy made out of a swarm of bees and is immune to your attacks. The GM is also free to have you fight equally overpowered supervilians.