RGB to HEX (and vice versa) converter
Two things jump out at me.


Decouple from the HTML elements.

var inputRgb = document.getElementById("rgb"),
    inputHex = document.getElementById("hex"),


I would do something like:

function RGB2Hex (inputRgb, inputHex){
    var converter = {
        toHex: ...
        toRGB: ...
    };

    inputRgb.addEventListener("input", converter.toHex, false);
    inputHex.addEventListener("input", converter.toRgb, false);

    return converter;
}

// Usage:
var mainHexConversion = new RGB2Hex(document.getElementById("rgb"), document.getElementById("hex"));
var secondHexConversion = new RGB2Hex(document.getElementById("mini-rgb"), document.getElementById("mini-hex"));

keep the background colour changing code outside the converter.

function RGB2Hex (inputRgb, inputHex, onColourChange)
{
   var converter = {
        toHex: ...
        toRGB: ...
        colourChanged: function(colourValue){
            if(typeof onColourChanged == "function")
            {
                onColourChange(colourValue);
            }
        }
    };
}

// Usage: 
var mainHexConversion = new RGB2Hex(
    document.getElementById("rgb")
    , document.getElementById("hex")
    , function(color)
    {
      document.body.style.backgroundColor = color;
    }
);