Great thread, here's my perspective:
My dad let my brother and me watch Star Trek with him for EVER.
Replace 'brother' with sister and this is my family. I am 4 years older than my sister... and one of my fondest memories (when my sister was still learning to hold her head up) is sitting on my dad's knee, watching Star Trek. It was a weekly ritual that I will always hold dear. Along with Star Trek I watched The X Files at a very young age, as well. My sister's first crush was on DD. We were desensitized at a very young age. And it was done with our parents in the same room. They were very diligent about explaining any questions we had... and I never remember being too scared to sleep, or any of that. And, the only thing that upset my sister was the episode Hush"¦ and, who can blame her? It was as if these shows provided a safe space for us, and our imaginations.
The whole reason we began watching Buffy is because the initial advertisements claimed it was from "the producers who brought you The X Files," or something to that effect. My sister was 8 at the time. We did grow up with it, and with XF and ST, as well. They are a part of my childhood, and I am proud of them, and of my parents, as well. We gained a lot of prospective from what we watched, and I believe it endowed us a balance of cynicism, realism, and morality; which combined with religion merged surprisingly easily.
At first my parents (mom, especially) were hesitant about us watching Buffy. I remember the first season my sister would be sent to bed early sometimes, unable to watch the show. However, that faded over time"¦ when my mother saw that the show was not causing any ill effects, and was drawing her daughters closer together. The show became a weekly ritual for the two of us, and we often discussed the shows in details"¦ including choices we disagreed with (Spike and Buffy's harmful relationship during season 6 being a big one). All in all, I think the decision needs to be decided on a family-by-family basis. Some children are able to assimilate the more graphic images that Buffy had to offer than others. However, there are obvious exceptions (many of which have already been mentioned).
And, if a family is unstable, and television viewing will not be monitored, than watching something harmful on television may be used as an escape from what is happening in the child's day to day life. This is by no means condoning that behavior, just a possibility.
On a final note: there is clearly no easy answer to this question, it is somewhere in the grey.