Only for ASCII text and does not contain validation. Inspired on Base64 Encoding Kata (thanks joseph.varnado to the kata)

base64_encode_decode.js

var Int6 = (function() {
  // Base64 ABC contains only A-Z, a-z, 0-9, + and /
  // (and the = sign but it's just a marker)
  var ABC = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
  return {
    toChar: function(e) { return ABC.substr(e, 1); },
    fromChar: function(e) { return ABC.indexOf(e); }
  };
}());

String.prototype.toBase64 = function() {
  // Split the string into characters
  // Convert each characer into a 8 bit binary number string
  // Join binary numbers
  var binary = this.split("").map(function(char) {
    var binary = char.charCodeAt().toString(2);
    return (new Array(9 - binary.length)).join(0) + binary;
  }).join("");
  
  // Calulcate how many extra bits are needed
  // and save the marker count
  var postfix = new Array(binary.length % 3 + 1).join('=');
  // Left padding zeros to fill the missing bits
  binary += new Array(binary.length % 3 * 2 + 1).join(0);
  
  // Split the final binary into 6 bits length strings
  // Get the 6 bit value (from Base64 ABC)
  // Join them and add the postfix (line 22)
  // Postfix sould be: "" (nothing), "=" and "=="
  return binary.match(/.{1,6}/g)
                .map(function(char) {
                  return Int6.toChar(parseInt(char, 2));
                })
                .join("") + postfix;
};

String.prototype.fromBase64 = function() {
  // Get the number of = signs at the end
  // Multiply by 2 to get the padding 0 bits
  var fixBits = (this.match(/=+$/g) || [""])[0].length * 2;
  // Remove the = signs
  // Split into characters
  // Get the Base64 ABC based index and convert into binary
  // Add the missing right padding zeros
  var binary = this.replace(/=+$/, "").split("").map(function(char) {
    var binary = Int6.fromChar(char).toString(2);
    return (new Array(7 - binary.length)).join(0) + binary;
  }).join("");
  
  // Remove left padding zeros based on line 40
  binary = binary.substr(0, binary.length - fixBits);
  
  // Split the final binary string into 8 bits length strings
  // Get the ASCII code of the given binary number
  // Join them to the final string
  return binary.match(/.{1,8}/g)
                .map(function(char) {
                  return String.fromCharCode(parseInt(char, 2));
                })
                .join("");
};