These are not your "happy ending" the "good guys win" kind of stories. Betrayal, corruption, class warfare, sacrifice and the hard realities of the human condition are laid bare in these books.
I'm really good friends with the author's son and we talk about the books a lot, he's never mentioned anything about Mormons. That doesn't mean that Mormons are definitely not a part of the story but it's not anything significant. The author and her family isn't Mormon either.
I've read them - no Mormony stuff I noticed. AFAIK, Suzanne Collins (the author) isn't Mormon. I think there has been some significant overlap with the Hunger Games fanbase and the Twilight fanbase.
I've read all three books and while I'm a nevermo, I consider myself well versed in the subject to be able to pick up on some of the intricacies should they appear.
I feel confident in saying that there is absolutely zero connection to Mormonism in Hunger Games. For one, Katniss (the heroine) has zero intention of ever marrying or having kids. The story revolves around a dystopian North America where one boy and girl are randomly selected from each district to "play" in the annual Hunger Games. The object is to kill and be the last one standing to win.
Think Orwell's 1984 meets a modern reality television program, like Survivor except with death. It's very dark and life is hard for every one involved. There is no religion. When people marry they "toast" (clink glasses?) each other and it's done. Katniss' family is impoverished, Katniss has to provide for her family by hunting and generally Katniss is very moody and distrusting of everyone (including the lead male, Peeta). She is not moody like Bella from Twilight. Bella was just obnoxious. Katniss is deservedly moody. She lives a nightmare of a life where people are killed just because and people are watched at all times.
I also read all three books. Found them quite enjoyable. Saw nothing that screamed "Mormon" to me. In fact, just the fact that the main character is a female and quite capable (a hero, in fact) tells me that it's completely lacking in Mormon themes. :)
I'm curious to know how it compares to Battle Royale, which seems to have a similar premise. Battle Royale's pretty disturbing, and a pretty deep, dark investigation into what humans do in desperation.
No Mormon connection. In fact I'd say the craze for this books in the Mormon world is rather hypocritical (not quite as bad as Twilight.) Hunger Games is super-violent; definitely R rated stuff in the book. It's almost as violent as to Bible, probably even more violent than the Book of Mormon.
I'm currently reading the third book. I kind of thought they were somewhat anti-mormon. The plot revolves around the ruling entity losing control and people thinking and acting for themselves in open rebellion.
I rather enjoyed the original version with Arnold Schwarzenegger and that guy from family feud. Don't see why we needed to remake it as a kid's film, book series.
I also don't want to see anything to do with the series, because I had a manipulative neighbor who kept trying to push them on me. Girl had all kinds of problems, and was always trying to guilt me into buying her junk off of her. At first I thought she was a cute girl, who was interested in me, but she was only interested in my wallet. Crazy as all get out too. Not the nice girl from work that I have been chasing, but crazy girl is probably why I was so worried about asking the nice girl out.
I live in Utah and I actually live with my in-laws who are Mormon/LDS and I have attended the church and researched the crap out of their church.
After reading the Hunger Games it is interesting to me to find people wondering if there is a Mormon base to it. No, there's not. There's not even a christian note to it. Nor is there any other religious stand point.