Being a real man = physical strength, emotional strength, financial strength.
What I mean: Physical strength = are you physically stronger than she is. Let's be honest; a woman would be embarrassed to be with a guy that she could beat arm wrestling. A woman still wants to feel like a woman. Every woman wants to be carried over the threshold, every woman wants to feel like a man is going to be able to provide security and protection. You don't have to be Arnold, but don't be a weakling.
Emotional strength: Do you know how and when to appropriately convey emotions? Can you be sensitive without breaking down and crying yourself? Women don't want men who cry at inappropriate times. An inappropriate time for a man to cry would be during a movie. You are supposed to be providing the strength and comfort to her. If you are breaking down more than she is, that is a definite turn off. But you don't need to remain stoic at the funeral of a person close to you. It is appropriate to grieve. Knowing how and when it is appropriate to show emotion, when is it appropriate to be vulnerable, and how you go about this is big. Having control of your emotions is big. You don't have to be Spock, but don't go breaking things and shouting over something minor.
Financial strength = are you able to live well within your means? Maybe you don't have the highest paying job, but are you doing fine with what you have? Are you going hungry because you're paying for your COMCAST DVR On-Demand? Women are more concerned with how well you are able to manage your finances rather than how much you make. You don't have to be Warren Buffet, but if you're only making $25K are you living well?
Just my thought...
You know, I read the first line and thought 'here we go again, I'm going to have to explain that I don't want someone to rescue me, I just want someone to love me."
But, after reading the rest of the post, I really do agree with it. Maybe I truly am an old-fashioned sexist pig, but I do appreciate a man that is stronger and more emotionally stable and able to take care of himself financially. And I'm sure he appreciates that I am concerned about his well-being even when he says he'll be okay (because we know you don't always mean it when you say that).
To me, a Real Man is one who is a good person and is reasonably comfortable with who he is. Someone who is willing to do the tough things because they are the right things. Someone who takes care of the people he loves (as I would do for him). My dad was a Real Man, and he's a tough act to follow, but I know they are out there because I've read their posts on these boards.
Now, I have to admit to being attracted to Manly Men. To me, that's a different thing. A Manly Man is probably a little old-fashioned in his view of male/female roles and works in a typical male occupation (firefighter, construction). I think every woman needs a Real Man, but my personal preference is for a Real Man that is also a Manly Man.