Ooh, this is just asking for a holy war, so let me fire the first salvo: Champions is evil. 
Seriously, while the Hero games have a very neat system for power design, the concept of every single skill having essentially its own rules and a bazillion derived attributes is so very 80s. More modern games achieve the same or better simulations with fewer rules.
For superheroics using a mainstream system, I'd recommend D20 Modern if you're into tactical combat or Aeonverse Storyteller (Trinity, Aberrant, Adventure!, and Exalted) if you or your players are more comfortable with Storyteller/WoD. If you're into more indie systems, Instant Fuzion and BESM could do the job -- this is actually one of the few genres for which BESM is well-suited. Godlike basically covers the sort of game you're after, but its system is awful. SAGA, if you can get ahold of it, might give you the feel you like, but bear in mind that it uses cards as its randomizer and that may not be everyone's cup of tea. GURPS, of course, is the worst system ever for running superpowers, and MEGS (Blood of Heroes) isn't much better. Torg/Masterbook would also be an unwise choice unless you like doing lots of math.
For something more realistic, where superbeings have more in common with touchy WMDs than with comic book characters, you might want to do some web searching. I'd recommend my own System X and the superpowered game I wrote for it, but that'd be just as bad as pimping my Wildcard system, based loosely on SAGA.
One problem with recommending game systems is that there are so many systems that work for any particular genre. Much of the choice of system, then, comes down to what sort of mechanics with which you and your group feel comfortable.
For superhero games specifically, I have not seen a lot of systems I would describe as great. Abberrant was better in my opionion than most, but the setting that goes with it might not mesh well with what you're going for.
There are a couple superhero d20 games out there, but d20 has never been my cup of tea.
If you just want to check out a cool game, look for anything associated with Greg Stolze. He's incredibly talented, and even if its not his personal project, he hardly ever gets involved with anything thats not brilliant. For a supers game he worked on, try "Godlike" which is set in WW2. My favorite game of his is called "Unknown Armies".
That being said,Stolze is really better at atmosphere, setting, and good writing than he is at game mechanics. The newer edition of Unknown Armies is a lot better about this.
For the new d20 hero systems i would recommend Mutants and Masterminds. Very fast paced fighting unlike Champions and a more consistent rules structure than the old Marvel Superhero game. The character creation is pretty simple but allows for almost any superhero build.
http://www.mutantsandmasterminds.com/
The game system has some flaws but really every one of them has something that has to be improved to some degree through house rules.
I always found Champions to be extremely easy to use.. Yeah there's TONS of possibilities. But the rules and conditions are always the same. You have your power, you konw what it does. You have your modifiers. They're all standard. Once you know the rules its so easy, and also seems by far to be the most customizable.
Tristat Silver Age Sentinals from Guardians of Order.
Flexible, easy to understand and points based.
From what Iunderstand Champions is very maths heavy. SAS isn't.
#2409 - The Mystery of the MAGI vaults. Azuria has contacted you to help her stop the thefts from the MAGI vaults.
#68054 - Out of the gutters. Left for dead, you swore that you were through with being a victim (alt villain beginning story)
Champions has a simple combat system. All powers are based on 11+ to hit from 3 dice.
The nice thing about Champoins (and why it might best suit your purpose) is that it represents all levels better than any other game I've played. By that I mean that using the same system you can have non-powered normals, pulp heroes and super heroes. They can all be different power levels, all using the same rules and can all mix up together.
The down side (as some have) is that the combat can be slow. However its always fun and very comic book.
Feel free to email me any questions you might have.
Yes. I think Champions has the most amount of flexibility over all the systems I've played. Combat seems slow and confusing, but it just takes a little getting used to is all. And knockback is fun. 
My favorite thing about Champions was the flexibility. No classes, no pre-defined powers, none of that. You paid points to buy results (x dice of damage, range, etc., mix and match) and you got to invent whatever you wanted that caused that result. The price list was comprehensive enough that you would be hard pressed to come up with a power or weapon that could not be described in game terms.
All this Champions talk, I agree it is a very flexible system and can be great for a Superhero game. One thing to consider is the setting he likes as the players will be more exceptional people verses actual superhuman there is always the Gurps system which focuses on skills and the actual super powers can be added in as the story progresses. The downside here is the Gurps system can be even more math intensive than champions. 2 cents...
First off, a shout-out to Tipsy_McStagger for bringing Unknown Armies onto the board. Easily the greatest role-playing game ever. But I'm sure its not what you need for your game (or even something you could get your head around - Most can't).
However since your needs are specific, Superheroes in 1910, I'd highly recommend ADVENTUE! from white-wolf. It has lots of useful background information and design for that time period. True, it's more pulp than four-color, but there are superpowers in it.
And if all else fails, I'd vote GURPS. Just do yourself a favor and stay away from d20 stuff like Mutants and Masterminds. You don't want to play a level-based system do you?
Oh wait...Security Levels...nevermind.
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And if all else fails, I'd vote GURPS. Just do yourself a favor and stay away from d20 stuff like Mutants and Masterminds. You don't want to play a level-based system do you?
Oh wait...Security Levels...nevermind.
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Well, Mutants and Masterminds is a points-based system making a token attempt to pretend to be level-based (and I won't get into the pros and cons of level-based sytems here...) My regular PnP group got burned out on their old (DC Heroes) campaign a few years back, but if I get the urge to run some superheroics again then Mutants and Masterminds is what I'd go for. For the original poster's requirements, I'd throw my vote in on the White Wolf Adventure! rules (based solely on what I've heard, not seen a copy yet).
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All this Champions talk, I agree it is a very flexible system and can be great for a Superhero game. One thing to consider is the setting he likes as the players will be more exceptional people verses actual superhuman there is always the Gurps system which focuses on skills and the actual super powers can be added in as the story progresses. The downside here is the Gurps system can be even more math intensive than champions. 2 cents...
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Thats the same reason why I'd recommend Champions! It has all the skills and talents needed for pulp, plus its easy to bring in powers as needed (mainly the villains )
I would suggest you use Villains and Vigilantes, but that would be showing my age a little too much. 
Seriously though, Champions and GURPS Supers are both fine systems. Can't say anything about the d20 M&M system, since I haven't played it. ((You young whipper-snappers and yer newfangled gaming systems!))
Most all of this has been mentioned, just resummarizing and giving my own opinions.
M&M is a fast-paced and terribly imbalanced beer and pretzel RPG. Good if you want to dive headlong into the action and don't mind imbalances between characters in your group.
Champions is a highly detailed basic grid upon which you can build virtually everything. However, the basic HERO rulebook is as thick as a phonebook and probably as dry to read the first time around. Once mastered though, I'd guarantee you that every player will get exactly the abilities they want without needing to rely on the GM too much.
This is not to be confused with Champions: The New Millenium which is based on the faster but vastly inferior Fuzion system. That said, I think TNM has the better background of the two games, but since it's set in the near future it won't help you.
GURPS is the same, to a lesser extent. The thing with GURPS is that the basic system is less well-defined, requiring more GM input during character creation and/or extra rulebooks treating the genre you're dealing with.
Adventure now is probably closest to what you're looking for. Set between the World Wars with three types of 'superheroes' (only one of which are classical superheroes in the sense of the Continuum -- Adventure is in its own timeline followed by Aberrant, a four colour superhero game and Aeon/Trinity, a Psi Powers SciFi game; Adventure offers the choice to play extremely skilled (or lucky) normal humans, proto-Novas (superbeings; they vaguely equate to the idea of Mutants as presented in X-Men) or proto-Psions.
It's a great game but heavily tied into the timeline of the three interlocking games and only a third of it is dedicated to actual superpeople. In other words, you might have to scrap some of it to make it fit your ideas.
I'd actually think Champions is what you want to go with, for several reasons. One, you can make absolutely sure every player gets what they want without imbalancing the game or your group. Two, it's easy to expand your abilities in many different ways. You said your players would start out relatively low-powered. Champions will allow your characters to grow in a completely non-linear fashion. Meaning you don't buy power X and as your character gains experience, all of power X's statistics increase a little bit. Rather, you can choose to invest in the power packing more well, raw power, or use it at a greater range, or over a wider area of effect. Other games offer similar ways of doing this, admitted, but none as thoroughly as Champions does.
To restate, Champions is the surefire way to let your players get exactly what they want. Only downfall is, it might take a bit of work to get there as everybody needs to get into the basics of the system.
"If you're going through hell, keep going."
Winston Churchill
Winston Churchill
Going to plug Silver Age Sentinals (Tristat version) again. ^^;;
Points based character creation.
Effects based power creation, e.g. there aren't seperate ice blast and fire blast powers, you'd buy 'Special attack, load it up with optional special effects and disabilities and say it's ice, fire, psionics or whatever.
Simple, fast combat with various options including knockback.
Scalable -- both by adusting the number of points used to build characters and the size of dice you roll.
#2409 - The Mystery of the MAGI vaults. Azuria has contacted you to help her stop the thefts from the MAGI vaults.
#68054 - Out of the gutters. Left for dead, you swore that you were through with being a victim (alt villain beginning story)
Read Champions in the shop before you make a decision on it.
Some love it (as has been said here)
A rare few are indefferent to it
Most roleplayers I know hate it (myself included)
YMMV
Check out the old Marvel Super Heroes RPG, that was fast and fun.
I like WW's Aberrant but it's fairly locked to the setting, However with that system you do get "Adventure!" for the pulp (1930-1940) setting.
I kind of liked the old "Super World" system in a masocistic way (very point based like Champions)
Oh and IMHO never touch GURPS with a 20ft bargepole, I have yet to see a setting it does well (which is strange as many of the sourcebooks are really informative, the system just sucks)
If you wnat a points based Xp system...
Silver Age Sentiniels d20 everything champions does but clearer and better thought out.
Plus great sections on running Super Heroes/villian and campaigns.
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I kind of liked the old "Super World" system in a masocistic way (very point based like Champions)
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Superworlds, if you can find a copy. The system inspired the Wild Cards books (hightly recomneded) Not to mention a vote for superworlds is a vote for Chaosium.
"Cthulhu for president, The Stars are right, Vote Mythos in 2004"
I am planning on starting a PnP Super Hero (Adventure First) game fairly soon, starting in 1915, where the players are the first Superheros in their world, although they will start with varely any powers, and more as people with amazing abilities, i.e. The Shadow.
For people that have played a lot of PnP R.P.G. what is the best system? At the moment I am leaning towards Champions, but is there a system that you love that you would sudgest?