How do I strip non-alphanumeric characters (including spaces) from a string?

In your regex, you have excluded the spaces from being matched (and you haven't used Regex.Replace() which I had overlooked completely...):

result = Regex.Replace("Hello there(hello#)", @"[^A-Za-z0-9]+", "");

should work. The + makes the regex a bit more efficient by matching more than one consecutive non-alphanumeric character at once instead of one by one.

If you want to keep non-ASCII letters/digits, too, use the following regex:

@"[^\p{L}\p{N}]+"

which leaves

BonjourmesélèvesGutenMorgenliebeSchüler

instead of

BonjourmeslvesGutenMorgenliebeSchler

You can use Linq to filter out required characters:

  String source = "Hello there(hello#)";

  // "Hellotherehello"
  String result = new String(source
    .Where(ch => Char.IsLetterOrDigit(ch))
    .ToArray());

Or

  String result = String.Concat(source
    .Where(ch => Char.IsLetterOrDigit(ch)));  

And so you have no need in regular expressions.

Or you can do this too:

    public static string RemoveNonAlphanumeric(string text)
    {
        StringBuilder sb = new StringBuilder(text.Length);

        for (int i = 0; i < text.Length; i++)
        {
            char c = text[i];
            if (c >= 'a' && c <= 'z' || c >= 'A' && c <= 'Z' || c >= '0' && c <= '9')
                sb.Append(text[i]);
        }

        return sb.ToString();
    }

Usage:

string text = SomeClass.RemoveNonAlphanumeric("text LaLa (lol) á ñ $ 123 ٠١٢٣٤");

//text: textLaLalol123