One idea which seems to be common, even among the non-religious, is that a religious upbringing is necessary to instill good values in children.
It's true that values come neatly packaged within many religions, and it's plausible that the belief in an Omnipresent God might be useful for preventing children from behaving badly in their parents' absence. Pragmatically speaking, though, religion is an imprecise tool for the task.
Religion as values-delivery package fails in two ways: first, it is overly broad, which may cause children to throw the values out if they don't agree with unrelated religious dogma; and second, religious people are vulnerable to having their values manipulated by religious figures and texts.
The first point is obvious: if a child is taught that one mustn't kill because God said so and later comes to believe that the Bible was written by men, then she might decide that murder is acceptable. Similarly, if she believes that the prohibition of eating milk and meat is silly, why refrain from stealing? Or, it could go the other way. Imagine a boy who is raised in a loosely religious household by parents who hold tolerance as an important value. If the boy decides to become more religious, he might be swayed by a religious figure or a book which extols discriminating against homosexuals.
The second point is a little less obvious since "religious values" are often thought to be consistent, at least within a particular religion. If you look at religion in practice, however, it's clear that two people of the same religion might hold completely opposite positions with regard to a particular value. Born again Christians are generally thought of as solidly Republican, but about a third of them consistently vote Democrat. Many Catholics enthusiastically support the Iraq war, while the Pope himself opposes it.
In short, religion is a bad tool for instilling values, and certainly not a necessary one. Parents must live their values, teach by example, and explain their value-beliefs to their children as well as they can.