How to find validity of a string of parentheses, curly brackets and square brackets?

With reference to the excellent answer from Matthieu M., here is an implementation in C# that seems to work beautifully.

/// <summary>
/// Checks to see if brackets are well formed.
/// Passes "Valid parentheses" challenge on www.codeeval.com,
/// which is a programming challenge site much like www.projecteuler.net.
/// </summary>
/// <param name="input">Input string, consisting of nothing but various types of brackets.</param>
/// <returns>True if brackets are well formed, false if not.</returns>
static bool IsWellFormedBrackets(string input)
{
    string previous = "";
    while (input.Length != previous.Length)
    {
        previous = input;
        input = input
            .Replace("()", String.Empty)
            .Replace("[]", String.Empty)
            .Replace("{}", String.Empty);                
    }
    return (input.Length == 0);
}

Essentially, all it does is remove pairs of brackets until there are none left to remove; if there is anything left the brackets are not well formed.

Examples of well formed brackets:

()[]
{()[]}

Example of malformed brackets:

([)]
{()[}]