Switching font and background color on button click
The repetition of getting a random font, color, background class cries to be extracted to a utility function:

function pickRandom(arr) { 
    return arr[Math.floor(Math.random() * arr.length)];
}

$("#try-me").click(function() {
    $("#content")
        .hide()
        .removeClass()
        .addClass(pickRandom(font))
        .addClass(pickRandom(color))
        .fadeIn(600);

    $("html")
        .removeClass()
        .addClass(pickRandom(background));
});


I also agree with @MainMa about defining background in terms of color.

Other than that, I think it's nice code!

Ensuring change

If you want to make sure that each font/color/background are different every time the user clicks on the button, then perhaps you can create another helper:

function pickRandomExcept(arr, previous) { 
    while (true) {
        var pick = arr[Math.floor(Math.random() * arr.length)];
        if (pick != previous) {
            return pick;
        }
    }
}


However, in the caller you will need to keep track of the previous picks of each. For example:

var picked_color;

$("#try-me").click(function() {
    picked_color = pickRandomExcept(color, picked_color);
    $("#content")
        .hide()
        .removeClass()
        .addClass(pickRandom(font))
        .addClass(picked_color)
        .fadeIn(600);