var desired = stringToReplace.replace(/[^\w\s]/gi, '')

As was mentioned in the comments it's easier to do this as a whitelist - replace the characters which aren't in your safelist.

The caret (^) character is the negation of the set [...], gi say global and case-insensitive (the latter is a bit redundant but I wanted to mention it) and the safelist in this example is digits, word characters, underscores (\w) and whitespace (\s).

What you need are character classes. In that, you've only to worry about the ], \ and - characters (and ^ if you're placing it straight after the beginning of the character class "[" ).

Syntax: [characters] where characters is a list with characters.

Example:

var cleanString = dirtyString.replace(/[|&;$%@"<>()+,]/g, "");

Use the string.replace() method and the unicode escape codes for your special characters. You have to use the \ character to escape in JavaScript regex

var str = 'Here is a \' string \" with \" \' some @ special ® characters ™ & &'
str.replace(/['"\u0040\u0026\u2122\u00ae]/g, '')

/pattern/ denotes a regex pattern in JavaScript

[charset] says which set of characters to match

/g specifies global matches so it will replace all occurrences

var mystring = "crt/r2002_2";
mystring = mystring.replace('/r','/');

will replace /r with / using String.prototype.replace.

Alternatively you could use regex with a global flag (as suggested by Erik Reppen & Sagar Gala, below) to replace all occurrences with

mystring = mystring.replace(/\/r/g, '/');

EDIT: Since everyone's having so much fun here and user1293504 doesn't seem to be coming back any time soon to answer clarifying questions, here's a method to remove the Nth character from a string:

String.prototype.removeCharAt = function (i) {
    var tmp = this.split(''); // convert to an array
    tmp.splice(i - 1 , 1); // remove 1 element from the array (adjusting for non-zero-indexed counts)
    return tmp.join(''); // reconstruct the string
}

console.log("crt/r2002_2".removeCharAt(4));

Since user1293504 used the normal count instead of a zero-indexed count, we've got to remove 1 from the index, if you wish to use this to replicate how charAt works do not subtract 1 from the index on the 3rd line and use tmp.splice(i, 1) instead.

Use the global flag:

var name = name.replace(/[^a-zA-Z ]/g, "");
                                    ^

If you don't want to remove numbers, add it to the class:

var name = name.replace(/[^a-zA-Z0-9 ]/g, "");

Using replace() with regular expressions is the most flexible/powerful. It's also the only way to globally replace every instance of a search pattern in JavaScript. The non-regex variant of replace() will only replace the first instance.

For example:

var str = "foo gar gaz";

// returns: "foo bar gaz"
str.replace('g', 'b');

// returns: "foo bar baz"
str = str.replace(/g/gi, 'b');

In the latter example, the trailing /gi indicates case-insensitivity and global replacement (meaning that not just the first instance should be replaced), which is what you typically want when you're replacing in strings.

To remove characters, use an empty string as the replacement:

var str = "foo bar baz";

// returns: "foo r z"
str.replace(/ba/gi, '');

It's working fine for me.
Working example: http://jsfiddle.net/JwrZ6/

It's probably your syntax, strings have to be defined with " around them.

var string = "xxxx † yyyy § zzzz";

NOT

var string = xxxx † yyyy § zzzz;

There are many different ways to tackle trimming strings, a regex is probably the most popular, and there are lots of blogs and performance tests out there, (one such blog), that you can look at and decide which is best.

So continuing along the lines that you have demonstrated, then this may be of some help to you.

Javascript

/*jslint maxerr: 50, indent: 4, browser: true */

var trim = (function () {
    "use strict";

    function escapeRegex(string) {
        return string.replace(/\[\{}?*+\^$\\.|\-]/g, "\\$&");
    }

    return function trim(str, characters, flags) {
        flags = flags || "g";
        if (typeof str !== "string" || typeof characters !== "string" || typeof flags !== "string") {
            throw new TypeError("argument must be string");
        }

        if (!/^[gi]*$/.test(flags)) {
            throw new TypeError("Invalid flags supplied '" + flags.match(new RegExp("[^gi]*")) + "'");
        }

        characters = escapeRegex(characters);

        return str.replace(new RegExp("^[" + characters + "]+|[" + characters + "]+$", flags), '');
    };
}());

/*jslint devel: true */

console.log(trim(" - hello** +", "+*- "));

On jsfiddle

Of course, you can customise which characters you wish to escape, or flags to test for, as per your own needs. Regular Expressions