First off, all our kids are different and will respond in different ways to being told their dx. Some will likely become anxious and worry about what it means. Many of you seem to have children who are oblivious to being different so it may be in those cases it's not necessary to share the dx. Others will benefit enormously from it.
My ds is almost 9, has had a dx of AS since he was 7 and a half, but had had three years of inconclusive assessments before we got to that stage. As a bright kid it was clear he was wondering why he was having all these hospital appointments when others weren't, and I felt it was important to explain to him. So he's probably one of the very few children who had AS explained to him before dx! I felt that was right for him because there were so obviously problems that needed to be dealt with in a particular way and it helped him to know that his mum and dad were trying to help him. He was visibly relieved when we told him there was a reason for his behaviour and the difficulties he was having, and he was reassured to know that we were doing our best for him.
Later, when we began on specific strategies to support him, it helped enormously that J understood the reasons why. With him 'on board' and knowing that he would ultimately benefit from checklists, timetables, token systems etc, he adapted to them and now (several years on!) takes them in his stride. In the last year we have worked intensively on managing his anger and he's come on in leaps and bounds, but I'm convinced he wouldn't have if he didn't know that such behaviour wasn't appropriate or that it was linked to his condition. He's not the same angry, confused and unhappy child he was a year ago.
The Kenneth Hall book (Asperger Syndrome, The Universe, and Everything) is lovely but it took me a while to read it to J because I felt it might upset him - he needed to develop his understanding to a certain level before the book would be of use to him. IIRC Kenneth went to a special school and was home-educated for a while - I didn't want J to assume that these things would happen to him as well, just because he had the same condition as Kenneth. A lovely book for understanding the dx from a child's point of view is Jude Welton's 'Can I Tell You About Asperger Syndrome'. I prefer it because it says things like "some people with AS don't like loud noises" etc but doesn't assume that everyone with AS is like that. It allows the child to decide for themselves how they're affected by the condition, which avoids the possibility of them assuming traits they don't have.
There are some excellent AS novels around too, where the main character has the condition and uses their autistic traits to help them solve crimes, mysteries etc (Kathy Hoopman has written a few).
I'm waffling now, and it's time to wake Beelzebub. Hope some of that helps.