Serializing object that contains cyclic object value

Use the second parameter of stringify, the replacer function, to exclude already serialized objects:

var seen = [];

JSON.stringify(obj, function(key, val) {
   if (val != null && typeof val == "object") {
        if (seen.indexOf(val) >= 0) {
            return;
        }
        seen.push(val);
    }
    return val;
});

http://jsfiddle.net/mH6cJ/38/

As correctly pointed out in other comments, this code removes every "seen" object, not only "recursive" ones.

For example, for:

a = {x:1};
obj = [a, a];

the result will be incorrect. If your structure is like this, you might want to use Crockford's decycle or this (simpler) function which just replaces recursive references with nulls:

function decycle(obj, stack = []) {
    if (!obj || typeof obj !== 'object')
        return obj;
    
    if (stack.includes(obj))
        return null;

    let s = stack.concat([obj]);

    return Array.isArray(obj)
        ? obj.map(x => decycle(x, s))
        : Object.fromEntries(
            Object.entries(obj)
                .map(([k, v]) => [k, decycle(v, s)]));
}

//

let a = {b: [1, 2, 3]}
a.b.push(a);

console.log(JSON.stringify(decycle(a)))

This is kind of an alternate-answer, but since what a lot of people will come here for is debugging their circular objects and there's not really a great way to do that without pulling in a bunch of code, here goes.

One feature that's not as well-known as JSON.stringify() is console.table(). Simply call console.table(whatever);, and it will log the variable in the console in tabular format, making it rather quite easy and convenient to peruse the variable's contents.