JSON is not just Object Notation
Until now, I've just considered JSON to be the equivalent to regular JavaScript object literal notation. Jonathan Snook has now explained the difference. It turns out JSON is a bit more picky than regular object literals. Key names must be quoted, and you can only use double-quotes around keys and values. Also, functions are not allowed as values.
I gave an example of JSON some time ago that turns out to be wrong. I used single-quotes in my JSON example. I'll leave them there since the example works, but I just can't call it JSON.
If you're doing JSON-style coding by hand for your Ajax communications, you can get away with using any object literals. So why care if it fits the JSON standard? Well, there are parsers and tools out there which can work with the JSON format, and if you don't fit the standard, they might not work.
I have no idea why the designers of JSON didn't just make the standard flexible enough to handle single quotes and unquoted keys. It's also confusing that JSON stands for JavaScript Object Notation, and that Object Notation somehow means something different from the object literal notation in JavaScript. Great.
Moral of the story: it probably doesn't matter if you use the JSON standard until you have to interoperate with JSON tools or feel the need to offer your JSON data to the public. You should probably stop calling it JSON if you use single-quotes, though.