I find the violence in the books and movies much less disturbing than the messages about women and about appropriate relationships. Both Bella and Edward are manipulative, controlling and emotionally abusive towards the other. Edward essentially stalks Bella, breaking into her house at night while she's sleeping. Finally, when they have sex the first time, Bella ends up covered with bruises. This is explained away as "he was so full of passion that he couldn't help hurting her", pretty much exactly the excuse most domestic abusers use.
On top of that the irony of it is that a prevailing theme in the book is that you can't choose who you love, and that one should pursue that love even if it's "forbidden" and then the author donates a significant portion of the profits to an organization that campaigns against marriage equality.
Finally, there the fact that the last book is written like very bad fanfiction of the first 3. It's truly one of the wackiest (but in an earnest 13 year old girl way, not a pushing the edges cool way) pieces of literature I've ever had the "pleasure" of reading.
Having said all that, my child, who is slightly vampire obsessed, asked to read them when he was 10 and so we read them together. I wanted to be able to discuss it as we read, and clarify my values and my expectations for him. The book wasn't out when he was 8, or if it was no one had heard of it yet, but if I had an 8 year old who was begging to see it, and talking about it with friends, I might take them just so that I could initiate conversations and reinforce my own values from the beginning.
I wouldn't take a 6 year old.