First, to allay any fears you might have, a superhero game is not unlike a high-level FRPG. The PCs are much more powerful than the average joe, but there are still challenges that require their immense power.
So, short answer- in order, I reccomend HERO System, Mutants & Masterminds or Godlike if you are a fairly experienced gamer, M&M, Godlike or HERO if you are relatively new to the hobby.
Why:
HERO is a point based system, and is my personal favorite (both the system in general and for supers in particular). Nothing quite matches it in flexibility and cross-genre consistency- there is absolutely no problem mixing superheroes, giant monsters, sorcerers, aliens or anything else. However, that flexibility comes at a cost- it is VERY rules/number crunching intensive. If you're a rules lawyer/PC tweeker or master thespian of any kind, your PC generation process can bog down in the myriad details that the system allows. Calculators are strongly advised, both for PC generation and game play. The main die used is the D6, and the more, the better.
However, Mutants & Masterminds, another point-based system, has quickly become my all-time #2 fave Supers game, vaulting ahead of others I've played & owned, like SAS D20, Brave New World, Heroes Unlimited/Cosmic Enforcers, Underworld, Aberrant/Aberrant D20 and Godlike.
Its nearly as flexible as HERO, but it has a lot flatter learning curve, esp. if you already have experience with any other D20 game (technically, its not D20, but its so close it doesn't matter). Plus, the setting is well done- Steve Kenson obviously took his time. HERO may simulate the comics better, but M&M's PC generation and combat systems are SO much more streamlined that a less experienced gamer cannot be scared off/disgusted by the game's complexity, a potential hazard with HERO.
My #3 favorite supers game is Godlike, and it has only 2 flaws as far as I'm concerned. There is a general lack of support publications available relative to other systems, and it is (so far) irrevocably tied to a WWII setting...although it handles that MAGNIFICENTLY. There are a lot of powers available, and this game is FLAVOR-RICH! Bonus: as far as I know, it is one of the only WWII RPG settings out there (I think GURPS has one). Its a D10 based game, with mechanics similar to Vampire, the Masquerade and the rest of the White Wolf Storyteller RPGs. There are also aspects of it that are similar to M&M, like Stunts and Extras that modify powers (called Talents) for example.