Update 2016 – five years on there are now new methods in the specs (see support below) to convert between strings and typed arrays using proper encoding.

TextEncoder

The TextEncoder represents:

The TextEncoder interface represents an encoder for a specific method,
that is a specific character encoding, like utf-8, iso-8859-2, koi8,
cp1261, gbk, … An encoder takes a stream of code points as input and
emits a stream of bytes.

Change note since the above was written: (ibid.)

Note: Firefox, Chrome and Opera used to have support for encoding
types other than utf-8 (such as utf-16, iso-8859-2, koi8, cp1261, and
gbk). As of Firefox 48 […], Chrome 54 […] and Opera 41, no
other encoding types are available other than utf-8, in order to match
the spec.*

*) Updated specs (W3) and here (whatwg).

After creating an instance of the TextEncoder it will take a string and encode it using a given encoding parameter:

if (!("TextEncoder" in window)) 
  alert("Sorry, this browser does not support TextEncoder...");

var enc = new TextEncoder(); // always utf-8
console.log(enc.encode("This is a string converted to a Uint8Array"));

You then of course use the .buffer parameter on the resulting Uint8Array to convert the underlaying ArrayBuffer to a different view if needed.

Just make sure that the characters in the string adhere to the encoding schema, for example, if you use characters outside the UTF-8 range in the example they will be encoded to two bytes instead of one.

For general use you would use UTF-16 encoding for things like localStorage.

TextDecoder

Likewise, the opposite process uses the TextDecoder:

The TextDecoder interface represents a decoder for a specific method,
that is a specific character encoding, like utf-8, iso-8859-2, koi8,
cp1261, gbk, … A decoder takes a stream of bytes as input and emits
a stream of code points.

All available decoding types can be found here.

if (!("TextDecoder" in window))
  alert("Sorry, this browser does not support TextDecoder...");

var enc = new TextDecoder("utf-8");
var arr = new Uint8Array([84,104,105,115,32,105,115,32,97,32,85,105,110,116,
                          56,65,114,114,97,121,32,99,111,110,118,101,114,116,
                          101,100,32,116,111,32,97,32,115,116,114,105,110,103]);
console.log(enc.decode(arr));

The MDN StringView library

An alternative to these is to use the StringView library (licensed as lgpl-3.0) which goal is:

• to create a C-like interface for strings (i.e., an array of character codes — an ArrayBufferView in JavaScript) based upon the
  JavaScript ArrayBuffer interface
• to create a highly extensible library that anyone can extend by adding methods to the object StringView.prototype
• to create a collection of methods for such string-like objects (since now: stringViews) which work strictly on arrays of numbers
  rather than on creating new immutable JavaScript strings
• to work with Unicode encodings other than JavaScript’s default UTF-16 DOMStrings

giving much more flexibility. However, it would require us to link to or embed this library while TextEncoder/TextDecoder is being built-in in modern browsers.

Support

As of July/2018:

TextEncoder (Experimental, On Standard Track)

 Chrome    | Edge      | Firefox   | IE        | Opera     | Safari
 ----------|-----------|-----------|-----------|-----------|-----------
     38    |     ?     |    19°    |     -     |     25    |     -

 Chrome/A  | Edge/mob  | Firefox/A | Opera/A   |Safari/iOS | Webview/A
 ----------|-----------|-----------|-----------|-----------|-----------
     38    |     ?     |    19°    |     ?     |     -     |     38

°) 18: Firefox 18 implemented an earlier and slightly different version
of the specification.

WEB WORKER SUPPORT:

Experimental, On Standard Track

 Chrome    | Edge      | Firefox   | IE        | Opera     | Safari
 ----------|-----------|-----------|-----------|-----------|-----------
     38    |     ?     |     20    |     -     |     25    |     -

 Chrome/A  | Edge/mob  | Firefox/A | Opera/A   |Safari/iOS | Webview/A
 ----------|-----------|-----------|-----------|-----------|-----------
     38    |     ?     |     20    |     ?     |     -     |     38

Data from MDN - `npm i -g mdncomp` by epistemex