Here are my thoughts.
While I love the characters in the HG trilogy at face value (I am firmly Team Peeta, BTW--he is my dream man) I think the true reason for the trilogy's popularity goes beyond even the great plot, characters, writing, etc.
It is the underlying theme, the basic sensitive, gentle and thoughtful nature of the author (who I met in person yesterday-swooooooon) that informs her ferocious story-telling skills. Suzanne Collins has something she wants to tell us. And her characters are more than just people. They are symbols.
Katniss is all of us--unsure, wanting to do good, but often mislead and used as a pawn in other people's agendas.
Snow, of course is just plain old base evil.
Gale--and this is controversial but I think after you've read the entire MG book you'll see my point. Gale is an example of how outrage, deprivation and abuse can make you a killer. Gale has become everything Katniss has tried to avoid. Gale is in transition to the point where he can become as bad as Coin, someone who might have started off as well-intentioned but lost sight of her moral compass. And this is what Katniss has always feared. And this is why things end so bad with Gale--no kissy-kissy. No closure. Katniss fears what Gale has become. What she might have become--if not for one person.
Which brings me to Peeta. Peeta is hope, beauty in the midst of chaos, love, everything that is good, that can still prevail even in the worst of circumstances. This is why when Peeta briefly turns bad it kills us (and Katniss) so much. Prim represents the same thing, but she is not as strong as Peeta. He is strength and beauty combined. SO in the end--Katniss had to choose Peeta. How could she not? He represents the hopeful future for humanity (and for her). Oh--and Haymitch. He's what you get when you are like Peeta, but without the hope. And Haymitch is whom Katniss might have become if she'd not found Peeta to remind her of why life is still worth living, even after you've survived the Hunger Games .