Depends on what you want as a 'strong' character. As this can be seen as strength of will, Strength of Ideals, or physical strength. You must decide what Strength 'is' before you can decide what a strong male character is. Personally I think it's a number of things, Physical strength so you can handle off threats, Intelligence to see your plans and Ideals through, and Strength of will to continue moving forward where others don't, whether this be in a simple task or a gigantic one. Now we go specifically to males. The only way to separate a strong female character and a male one is to see what is generally, and naturally different. So basically, what Testosterone gives. It breeds confidence, which goes hand in hand with leadership. It brings physical prowess, as it increases muscle mass and density. It brings aggression, which is specifically a bad trait, especially if one can control and channel it. It also makes one quite horny, so many men as often can see, also see this as a good thing(I'm indifferent on this, not my thing, but go for it. Your life). So Leadership, Confidence, Physical Prowess, Aggression and Promiscuous. While women of course, CAN be all of these things, Men, Naturally, and in general, have a more likelihood of doing so. And this can be seen with alot of old action heroes with these five traits as well. However me personally. I believe a strong man is someone who can take a beating(Physical or emotional) and continue fighting, until he's either dead in the ground, or succeeded. Someone who takes responsibility for his actions, and Takes care of his family(if he has one). When I think of strong men, I think of people like Wolverine, Geralt of Rivia, Gutts from Berserk, or Captain America. Strong doesn't specifically mean "Good" of course, But they're what I think of, I suppose you could also say, Men like Tywin Lannister, for a strong male antagonist. His intellect and ruthlessness, definitely shows that, along with great leadership and confidence.
Someone mentioned Ellen Ripley. I don't think she has any direct bearing on this topic because she isn't male, but she provides a useful contrast because she is often held up as the de facto example of a strong, female protagonist. The thing I believe is important about her is that her function in the story is entirely different from that of, say, Hicks, or even Vasquez (who is also biologically, but not socially, female). The critical difference is that her role is to survive, not to sacrifice. Dying makes a man strong. Living makes a woman strong. This is a result of our unequal societal expectations of the two (which, of course, result from unequal biological imperatives). Edit: I suppose, having made these thoughts explicit, that I must now confess that the entire point of my work in progress (working title "Sacrifice") is to reverse these roles.
Famous male heroes who die: Achilles, J.C, Braveheart, King Arthur, Beowulf, Caesar Famous male heroes who live: James Bond, majority of LOTR fellowship members, Odysseus, Robin Hood, most famous comic book characters, the Time Traveler, most Schwarzenegger roles, most Dwayne Johnson roles I'm not seeing any clear trends here
I think if you remove "well-written" from your criteria, you open things up to a lot of shallow work with one-sided, almost comic-book improbable characters, like superheroes. I would suggest that most "strong" characters are more complex than the actions others see, more than their acts of courage. Is that what you mean by saying that the media won't portray them? I think that's a sign of recognition of the human character, that there are no heroes, only people who do heroic things. You could say that Sherlock Holmes is fearless but I don't think he is really well-developed. He's weak in that he is subject to cocaine and he's flawed in that he doesn't usually exhibit much compassion or understanding of the humanity of most of his clients. PD James' Dagleish is another. He is fearless, but not necessarily heroic. Or maybe the protagonist in Cuckoo's Nest, fearless in that he refuses to fold. Or the Native American guy in the book -- Chief -- who ultimately throws the table out the window and walks away. Brave, but flawed. Maybe the lead in Braveheart, who fought a brave but doomed fight, He was brave, but I'd suggest obsessed and thereby imperfect.
The problem here is the definition of the word 'strong' and how it applies. There are different types of strength. The most obvious is physical strength, then there's mental strength, emotional strength, spiritual strength, moral strength. It really all depends on the context of the character and the situation they find themselves in. While someone might be 'strong' in one situation, they might come up weak in another. John Rambo is a good example. When it comes to fighting and ass kickery, he's about as strong as they come. On the other hand I really don't see him sitting down with a cup of hot cocoa and talking about his feelings with other people around a campfire.
The other problem is deciding how the word modifies "character". Do we mean a character who's a strong person, or a character who's strongly, vividly portrayed, regardless of his personal characteristics? It's far from precise terminology.
