As has been pointed out: Mutants & Masterminds for the win. It's not only a good midpoint between flexibility and user-friendliness, but it kind of scales up in complexity according to what you want to do with it. If you want a near-Hero System level of control, it's there, but you don't actually have to go that deep into it if you don't want to generate characters on multi-page Excel spreadsheets (although there's
a really great one out there, if you do). Basically anybody who can handle point-based character generation should be able to put together an extremely unique character without having to resort to special software.
The powers system is effects based, so instead of having a "claws" power, there's Strike, which gives you a damage bonus on melee attacks, and it's up to you whether that represents claws, electrified hands, a baseball bat, or what (and, of course, all kinds of modifiers can be applied to make claws, electrified hands, and baseball bats mechanically different). So modelling inherent powers, gadgets, magic, special training, etc. is no problem at all.
It's an OGL system, with a few recognizeable D&D 3E trappings, but the resolution system is completely based on rolling a single d20; no other dice are used at all. Combat doesn't revolve around hitpoints, but instead a saving throw mechanic by which characters try to resist the effects of attacks that hit them. Better yet, it's not a pass-fail resolution, but instead allows for different levels of injury from an attack depending on how badly the target fails the save. Most NPCs in the game are classed as "minions", meaning that one failed toughness save, and they're out of the fight, so scenes where the heroes plow through hordes of mooks are expected. Non-minion characters--like the PCs and major villains--can take a hit, but suffer a cumulative penalty on future toughness saves (and, if they're hurt enough, on other things).
Hero points are used extensively as a reward (and sometimes a consolation prize) for PCs. They're expected to be awarded and spent a lot faster than Eberron's action points, and can also do a bit more than action points can.
The game is easily adjustable to different power levels of characters and lethality levels of combat, and a lot of optional rules are presented to customize your campagin further. And, like any good superhero system, it can handle other genres, as well: I wouldn't hesitate to use it for fantasy, sci-fi, horror, whatever. I've actually played a Planescape game using the M&M system, and it let us create more appropriately-bizarre characters than old AD&D 2E ever could have (the psychic rebel githyanki was the boring one). Someday, I'd like to try using M&M for a World of Darkness (-ish) game.