I pretty much like the idea of hdogan, but there's at least one group of characters he's missing: ligature characters.
They're at least used in Norwegian and I read something about French, too ... Some are just used for styling (f.e. fi)

Here's an example that supports all characters (should at least, according to the documentation):
<?php
var_dump(transliterator_transliterate('Any-Latin; Latin-ASCII; Lower()', "A æ Übérmensch på høyeste nivå! И я люблю PHP! fi"));
// string(41) "a ae ubermensch pa hoyeste niva! i a lublu php! fi"
?>

In this example any character will firstly be converted to a latin character. If that's finished, replace all latin characters by their ASCII replacement.

Sorry, for posting it again, but I found a bug in my code:

If you have a character, like the cyrillic ь (a soft-sign - no sound), the "Any-Latin" would translate it to a prime-character, and the "Latin-ASCII" doesn't touch prime-characters. Therefore I added an option to remove all characters, that are higher than \u0100.

Here's my new code, including an example:

var_dump(transliterator_transliterate('Any-Latin; Latin-ASCII; [\u0100-\u7fff] remove',
    "A æ Übérmensch på høyeste nivå! И я люблю PHP! есть. fi"));
// string(50) "A ae Ubermensch pa hoyeste niva! I a lublu PHP! est. fi"

Another approach, I found quite helpful (if you by no way want to remove characters ...), try to use iconv() in addition. This surely will just return ASCII characters.

See: http://stackoverflow.com/a/3542748/517914

Also an example here:

var_dump(iconv("UTF-8", "ASCII//TRANSLIT//IGNORE", transliterator_transliterate('Any-Latin; Latin-ASCII',
    "A æ Übérmensch på høyeste nivå! И я люблю PHP! есть. fi"));
// string(50) "A ae Ubermensch pa hoyeste niva! I a lublu PHP! est'. fi"

You can create slugs easily with:

<?php
function slugify($string) {
    $string = transliterator_transliterate("Any-Latin; NFD; [:Nonspacing Mark:] Remove; NFC; [:Punctuation:] Remove; Lower();", $string);
    $string = preg_replace('/[-\s]+/', '-', $string);
    return trim($string, '-');
}

echo slugify("Я люблю PHP!");
?>

There are some possibly undesirable conversions with ASCII//TRANSLIT//IGNORE or your users may require some custom stuff.

You might want to run a substitution up front for certain things, such as when you want 3 letter ISO codes to replace currency symbols. £ transliterates to "lb", for example, which is incorrect since it's a currency symbol, not a weight symbol (#). 

ASCII//TRANSLIT//IGNORE does a great job within the realm of possibility :-)

When it doesn't do something you want it to, you can set up a CSV with one replacement per line and run a function like:

    function stripByMap($inputString, $mapFile)
    {
        $csv = file($mapFile);
        foreach($csv as $line)
        {
            $arrLine = explode(',', trim($line));
            $inputString = str_replace($arrLine[0],$arrLine[1],$inputString);
        }
        return $inputString;
    }

or you can write some regexes. Transliterating using ASCII//TRANSLIT//IGNORE  works so well that your map probably won't be very long...