Related questions:
The iconv module can do this, more specifically, the iconv() function:
$str = iconv('Windows-1252', 'ASCII//TRANSLIT//IGNORE', "Gracišce");
echo $str;
//outputs "Gracisce"
The main hassle with iconv is that you just have to watch your encodings, but it's definitely the right tool for the job (I used 'Windows-1252' for the example due to limitations of the text editor I was working with ;) The feature of iconv that you definitely want to use is the //TRANSLIT flag, which tells iconv to transliterate any characters that don't have an ASCII match into the closest approximation.