I worked from the initially posited question: "... if you ask a civilian to start naming superheroes, who's the first non-Marvel or DC character they mention?"

The Incredibles IS a very recent, non-Marvel or DC super hero property that was plenty popular. There might be cartoons on TV with super heroes, but I don't see those right now - not that I wouldn't watch. I just don't catch much Nickelodeon or Disney Channel.

As for what constitutes a super hero... first, OUR opinions are very different from civilian knowledge of supers. Ask me to think of a super hero that isn't DC or Marvel, and you might get Captain Hero or Purehart the Powerful; you might get Cerebus; you might get Mr. Incredible; or you might get a dozen others. If I ask Mr. Byrne, Robbie P., or one of our British oriented friends, it could be Dan Dare.

But the man on the street, I feel, mostly A) remembers what he's seen most recently, and B) thinks of abilities above and beyond those of mortals as a "super hero." So they might well pick James Bond, or Mr. Spock, or Harry Potter as I suggested. Nobody here would pick one of them as a super hero; but we're not the targets.

And let us not forget that the standard person's idea of super heroes and their companies is VERY limited. They may not know that the Fantastic Four, Deadpool, Ghost Rider, Howard the Duck, and Spider-Man are all Marvel properties.

Of course, so many might just say, "What do you mean, Marvel or DC? Isn't there just one companies that does super heroes?" We ascribe a lot of our knowledge to those not nearly as interested in comics. They might not know, or care.

Seriously, though, it's so hard to think of Dan Dare or James Bond as superheroes even though they perform feats better than us mere mortals. Yet at the same time, if we "disqualify" them on that basis, do we disqualify Captain America?

Of course we don't. Cap is a superhero. But one could argue that, lack of a super-soldier serum aside, Dare and Bond perform feats that are superior to a normal person.

A specific costume is usually in the mix, rather than simply a recurring outfit as with Tarzan, Popeye, or Little Orphan Annie. Masks and capes are a plus. An intention to go out and fight crime or evildoers is a generally accepted element, as is a secret identity and a separate name under which one is known while performing super-heroic feats. Another qualifying element is living in a world or a context in which super-heroes exist and are an acknowledged phenomenon. 

Pulp heroes such as Doc Savage, the Shadow, and the Spider all very nearly qualify, but may not by some people's definition since they exist within a separate context from the sort of fantastic premises shown in DC or Marvel comics. Doc Savage is not likely to battle actual space aliens or take a trip to Asgard. The Shadow is not likely to wind up confronting a criminal mastermind who is piloting a giant robot. Their realities are more restrictive and often more violent. Guns are relied upon to much greater degree, and the heroes generally do not adhere to a moral code that prohibits them from killing their opponents.  

Many of the elements are there, and there is no question such characters, along with the Pimpernel and Zorro, were immensely influential upon the imaginations of those who would go on to create the comic book super-heroes, but they're still essentially adventure characters rather than super-heroes. 

Somehow, the visual is crucial to unquestioned acceptance within the super-heroic community. Tarzan is an adventure character, but the Phantom is a super-hero, although both operate under similar circumstances. Somehow the Phantom's costume and mask put him over the top, whereas Tarzan is going to remain an adventurer alongside Flash Gordon and Mandrake, regardless of how fantastical their surroundings become. 

Zatara, a Mandrake clone, gets grandfathered into the super-hero world by virtue of his team-ups with them and his daughter's active involvement in the Justice League. Lois Lane and Jimmy Olsen have assumed super-heroic identities in the past and certainly live in a world filled with such individuals, but on their own, neither is a super-hero unless they're in costume. Flamebird and Elastic Lad are super-heroes, but Jimmy usually is not. Neither is Jarvis or Commissioner Gordon. They all know a lot of super-heroes and occasionally take to the streets in various disguises to seek justice, but overall, not everyone gets to call themselves a super-hero, just because they live in a world filled with them.

Are these absolutes? Of course not. You can point to the issue of Brave and the Bold wherein Batman teams up with Lois who is shown swinging in on a rope to take on Metallo and say, "Well, she's clearly a super-hero in this comic," and I'd see your point, but nevertheless maintain that she is not. Was Barbara Gordon a super-hero while she was Oracle? I'd say yes, since she maintained a double identity, headed a team of costumed crimefighters, and pursued super-heroic activities as a primary part of her existence, even if she couldn't go out into the streets herself. Is Charles Xavier a super-hero? Again, I'd say yes, since he himself possesses super-powers, heads a team of super-heroes, and has battled alongside them while struggling to keep their identities hidden from the general public. How about Danny Chase? Yep; member of a super-team, powers, and it's his primary purpose in the story to fight alongside the costumed good guys to stop the bad. He'd have put on a costume and taken a super-hero name eventually, theoretically. Same with Doug Ramsey... He was hardly an effective super-hero in regular combat, but his reason to exist in the narrative was to have him as a member of the New Mutants, fighting the bad guys in the best way he knew how.

Adventurers, particularly those in masks with colorful names such as the Pimpernel and Zorro, unquestionably set the stage for what was to come, but I don't believe that they themselves meet the aggregate requirements to join the super-heroic community. While Batman is very nearly the same sort of character they are, his world immediately involved vampires & monster men and would go on to include interplanetary adventures and Kryptonian super-pals. Context is important. 

I think a secret identity would be a qualifying factor for me. The Turtles don't have secret identities so that doesn't make them heroes. Of course, there are DC and Marvel super heroes that don't have secret identities - so that's my logic screwed! 

And, yes, the Lone Ranger wears a mask, but he doesn't have "civilian adventures" where he hangs round the Wild West equivalent of the Coffee Bean Bar. Has his real name even been mentioned? So he has a mask, but whoever he is, the civilian identity isn't a factor (I guess he must have one, though, for when the Lone Ranger mask and outfit has to go to the laundry!). 

I can get behind the term "adventure heroes" for the likes of Bond and the Scarlet Pimpernel.

Some years ago, I remember a Family Feud episode (Richard Karn era) where one survey was "Name a Sexy Superhero." The usual suspects were all run through but there was one slot left and nobody could guess it. At the end it was revealed to be "James Bond." ... Civillians.