I don't have kids, but if I did I would let them watch the Simpsons. I am a firm believer in teaching kids to let their imagination run wild but also to teach them a strong understanding between fiction and reality.
I don't have kids, but I was allowed to watch the show when I was younger. Since then, however, I think the episodes have become more adult, and not appropriate for children's viewing. There are some episodes I would be happy to let kids watch, but many more that I wouldn't.
My kids don't watch commercial tv because I'd rather avoid the ads until they're a bit older but if they were watching it I'd let them watch the Simpsons. I don't think they'd really like it though. They're a bit too young.
I think I'd let my son watch the Simpsons when he gets older, perhaps around 12. Many episodes do have sexual references, and that I don't like. Besides, I think it is a show that cannot be appreciated at a very young age.