One of the hassles I regularly experience with JavaScript is that it does not have native support for supplementary characters.  Internally, JavaScript uses UCS-2 encoding (unlike most of the rest of the web, which uses UTF-8…)  While you can use surrogate pairs to represent Unicode characters between U+10000 and U+10FFFF, this makes string handling with these characters a pain.  In particular, functions such as indexOf and substr have to be very carefully used, both to account for the surrogate pairs in their index parameters, and to avoid cutting them in half when manipulating the string. Of course, when interfacing with third party services, you will need to be aware of how they handle text.  For instance, the Twitter 140 character limit counts Unicode code points, not UCS-2 code units.  But many other products, (for example, Microsoft SQL Server), use UTF-16 or UCS-2 internally and treat supplementary plane characters as 2 code units for the purposes of calculating field size.  Developer beware! Anyway, I have put together a small set of functions that treat surrogate pairs as a single code point, abstracting away surrogate pairs at the basic String level.  Adding support for surrogate pairs is not a complete solution — I haven’t done any work on regular expressions, for example, and this code also does not begin to address more complex requirements around grapheme clusters or normalisation, but this is just one less complexity to worry about. The functions do not replace any existing String functions. This code is not complete: I am missing some boundary conditions and edge cases, and I haven’t yet tested with isolated surrogate code units — but for what it’s worth, here it is.  The kmw prefix refers to KeymanWeb, which will shortly be using the functions (replacing the mishmash of code we currently use…) Some simple examples:

var str="Brave "+String.kmwFromCharCode(0x13027, 0x1314C, 0x1309C)+" world";

alert(str.indexOf("w"));    // Displays 13
alert(str.kmwIndexOf("w")); // Displays 10

alert(str.length);       // Displays 18
alert(str.kmwLength());  // Displays 15

alert(str.kmwSubstr(4,3));  // Displays e U+13027
alert(str.substr(4,3));  // Displays e U+D80C (half a supplementary pair!)

The license on this code is Mozilla Public License 1.1.  A couple of functions were lifted from the proposal Supplementary Characters for ECMAScript by Norbert Lindenberg and tweaked (back) to more closely mimic the functions they replace, warts and all.  These two functions are probably better tested than my ones! Version 1.0 of this library plus a rudimentary test script can be downloaded from http://durdin.net/blog-files/kmwString-0.1.zip. Comments, bug fixes, flames, suggestions much appreciated!

/**
  @preserve (C) 2012 Tavultesoft Pty Ltd
  
  Adds functions to treat supplementary plane characters in the same 
  way as basic multilingual plane characters in JavaScript.
  
  Version 0.1
  
  License
  
  The contents of this file are subject to the Mozilla Public License
  Version 1.1 (the "License"); you may not use this file except in
  compliance with the License. You may obtain a copy of the License at
  http://www.mozilla.org/MPL/

  Software distributed under the License is distributed on an "AS IS"
  basis, WITHOUT WARRANTY OF ANY KIND, either express or implied. See the
  License for the specific language governing rights and limitations
  under the License.

  The Original Code is (C) 2012 Tavultesoft Pty Ltd.

  The Initial Developer of the Original Code is Tavultesoft.
*/

/**
 * Constructs a string from one or more Unicode character codepoint values 
 * passed as integer parameters.
 * 
 * @param  {integer} cp0,...   1 or more Unicode codepoints, e.g. 0x0065, 0x10000
 * @return {String}            The new String object.
 */
String.kmwFromCharCode = function() {
  var chars = [], i;
  for (i = 0; i < arguments.length; i++) {
    var c = Number(arguments[i]);
	if (!isFinite(c) || c < 0 || c > 0x10FFFF || Math.floor(c) !== c) {
	  throw new RangeError("Invalid code point " + c);
	}
	if (c < 0x10000) {
	  chars.push(c);
	} else {
	  c -= 0x10000;
	  chars.push((c >> 10) + 0xD800);
	  chars.push((c % 0x400) + 0xDC00);
	}
  }
  return String.fromCharCode.apply(undefined, chars);
}

/**
 * Returns a number indicating the Unicode value of the character at the given 
 * code point index, with support for supplementary plane characters.
 * 
 * @param  {integer} codePointIndex  The code point index into the string (not 
                                     the code unit index) to return
 * @return {integer}                 The Unicode character value
 */
String.prototype.kmwCharCodeAt = function(codePointIndex) {
  var str = String(this);
  var codeUnitIndex = 0;
  
  if (codePointIndex < 0 || codePointIndex  >= str.length) {
    return NaN;
  }

  for(var i = 0; i < codePointIndex; i++) {
    codeUnitIndex = str.kmwNextChar(codeUnitIndex);
	if(codeUnitIndex == undefined) return NaN;
  }
  
  var first = str.charCodeAt(codeUnitIndex);
  if (first >= 0xD800 && first <= 0xDBFF && str.length > codeUnitIndex + 1) {
    var second = str.charCodeAt(codeUnitIndex + 1);
	if (second >= 0xDC00 && second <= 0xDFFF) {
	  return ((first - 0xD800) << 10) + (second - 0xDC00) + 0x10000;
	}
  }
  return first;  
}

/**
 * Returns the code point index within the calling String object of the first occurrence
 * of the specified value, or -1 if not found.
 * 
 * @param  {string}  searchValue    The value to search for
 * @param  {integer} fromIndex      Optional code point index to start searching from
 * @return {integer}                The code point index of the specified search value
 */
String.prototype.kmwIndexOf = function(searchValue, fromIndex) {
  var str = String(this);
  var codeUnitIndex = str.indexOf(searchValue, fromIndex);
  
  if(codeUnitIndex < 0) {
    return codeUnitIndex;
  }
  
  var codePointIndex = 0;
  for(var i = 0; i < codeUnitIndex; i = str.kmwNextChar(i), codePointIndex++);
  return codePointIndex;
}

/**
 * Returns the code point index within the calling String object of the last occurrence 
 * of the specified value, or -1 if not found.
 * 
 * @param  {string}  searchValue    The value to search for
 * @param  {integer} fromIndex      Optional code point index to start searching from
 * @return {integer}                The code point index of the specified search value
 */
String.prototype.kmwLastIndexOf = function(searchValue, fromIndex)
{
  var str = String(this);
  var codeUnitIndex = str.lastIndexOf(searchValue, fromIndex);
  
  if(codeUnitIndex < 0) {
    return codeUnitIndex;
  }
  
  var codePointIndex = 0;
  for(var i = 0; i < codeUnitIndex; i = str.kmwNextChar(i), codePointIndex++);
  return codePointIndex;
}

/**
 * Returns the length of the string in code points, as opposed to code units.
 * 
 * @return {integer}                The length of the string in code points
 */
String.prototype.kmwLength = function() {
  var str = String(this);
  
  if(str.length == 0) {
    return 0;
  }
  
  for(var i = 0, codeUnitIndex = 0; codeUnitIndex != undefined; i++, 
    codeUnitIndex = str.kmwNextChar(codeUnitIndex));
  return i;
}

/**
 * Extracts a section of a string and returns a new string.
 * 
 * @param  {integer} beginSlice    The start code point index in the string to 
 *                                 extract from
 * @param  {integer} endSlice      Optional end code point index in the string
 *                                 to extract to
 * @return {string}                The substring as selected by beginSlice and
 *                                 endSlice
 */
String.prototype.kmwSlice = function(beginSlice, endSlice) {
  var str = String(this);
  var beginSliceCodeUnit = str.kmwCodePointToCodeUnit(beginSlice);
  var endSliceCodeUnit = str.kmwCodePointToCodeUnit(endSlice);
  return str.slice(beginSliceCodeUnit, endSliceCodeUnit);
}

/**
 * Returns the characters in a string beginning at the specified location through
 * the specified number of characters.
 * 
 * @param  {integer} start         The start code point index in the string to 
 *                                 extract from
 * @param  {integer} length        Optional length to extract
 * @return {string}                The substring as selected by start and length
 */
String.prototype.kmwSubstr = function(start, length)
{
  var str = String(this);
  if(start < 0)
  {
    start = str.kmwLength() + start;
	if(start < 0) {
	  start = 0;
	}
  }
  var startCodeUnit = str.kmwCodePointToCodeUnit(start);
  var endCodeUnit = startCodeUnit;
  
  if(length == undefined) {
    endCodeUnit = str.length;
  } else {
    for(var i = 0; i < length; i++, endCodeUnit = str.kmwNextChar(endCodeUnit));
  }

  return str.substring(startCodeUnit, endCodeUnit);
}

/**
 * Returns the characters in a string between two indexes into the string.
 * 
 * @param  {integer} indexA        The start code point index in the string to 
 *                                 extract from
 * @param  {integer} indexB        The end code point index in the string to 
 *                                 extract to
 * @return {string}                The substring as selected by indexA and indexB
 */
String.prototype.kmwSubstring = function(indexA, indexB)
{
  var str = String(this);
  
  if(indexA > indexB) { var c = indexA; indexA = indexB; indexB = c; }
  
  var indexACodeUnit = str.kmwCodePointToCodeUnit(indexA);
  var indexBCodeUnit = str.kmwCodePointToCodeUnit(indexB);
  if(isNaN(indexBCodeUnit)) indexBCodeUnit = str.length;

  return str.substring(indexACodeUnit, indexBCodeUnit);
}

/*
  Helper functions
*/

/**
 * Returns the code unit index for the next code point in the string, accounting for
 * supplementary pairs 
 *
 * @param  {integer} codeUnitIndex   The code unit position to increment
 * @return {integer}                 The index of the next code point in the string,
 *                                   in code units
*/
String.prototype.kmwNextChar = function(codeUnitIndex) {
  var str = String(this);
  
  if(codeUnitIndex < 0 || codeUnitIndex >= str.length - 1) {
    return undefined;
  }
  
  var first = str.charCodeAt(codeUnitIndex);
  if (first >= 0xD800 && first <= 0xDBFF && str.length > codeUnitIndex + 1) {
    var second = str.charCodeAt(codeUnitIndex + 1);
	if (second >= 0xDC00 && second <= 0xDFFF) {
	  if(codeUnitIndex == str.length - 2) {
	    return undefined;
	  }
	  return codeUnitIndex + 2;
	}
  }
  return codeUnitIndex + 1;
}

/**
 * Returns the code unit index for the previous code point in the string, accounting
 * for supplementary pairs 
 *
 * @param  {integer} codeUnitIndex   The code unit position to decrement
 * @return {integer}                 The index of the previous code point in the
 *                                   string, in code units
*/
String.prototype.kmwPrevChar = function(codeUnitIndex) {
  var str = String(this);

  if(codeUnitIndex <= 0 || codeUnitIndex > str.length) {
    return undefined;
  }
  
  var second = str.charCodeAt(codeUnitIndex - 1);
  if (second >= 0xDC00 && first <= 0xDFFF && codeUnitIndex > 1) {
    var first = str.charCodeAt(codeUnitIndex - 2);
	if (first >= 0xD800 && second <= 0xDBFF) {
	  return codeUnitIndex - 2;
	}
  }
  return codeUnitIndex - 1;
}

/**
 * Returns the corresponding code unit index to the code point index passed
 *
 * @param  {integer} codePointIndex  A code point index in the string
 * @return {integer}                 The corresponding code unit index
*/
String.prototype.kmwCodePointToCodeUnit = function(codePointIndex) {
  var str = String(this);
  
  var codeUnitIndex = 0;

  if(codePointIndex < 0) {
    codeUnitIndex = str.length;
    for(var i = 0; i > codePointIndex; i--, 
	  codeUnitIndex = str.kmwPrevChar(codeUnitIndex));	
    return codeUnitIndex;
  }

  for(var i = 0; i < codePointIndex; i++,
    codeUnitIndex = str.kmwNextChar(codeUnitIndex));
  return codeUnitIndex;
}

Updated 11 May 2012: Removed script formatting code as site hosting it was unreliable. Back to good old <pre> for now.
Updated 29 May 2014: Fixed broken script text, damaged when inserted previously.