Worked until about November 2012, then Mozilla destroyed it by an update. Now I've got a workaround: Open new window with contents to copy inside.
Thanks to Matthew Flaschen for the DataURL idea (https://stackoverflow.com/a/3665147/1120146)
/**
*   To use the clipboard from Mozilla / NS / Firefox:
*
*   Clipboard access works only up to Firefox 14 :-( (thanks to those security fanatics)
*
*   Solution for later versions: Window pops up with text inside (data url)
*   
*   In "about:config" : 
*       set signed.applets.codebase_principal_support = true!
*
*   @param text: The text which shold be copied to clipboard
*   @param fallbackContentType: The content type of the text, if clipboard access 
*                               doesn't work, i.e. "text/csv"
*                               default: text/plain
*/
function toClipboard(text, fallbackContentType) {
    var success = false;
    if (window.clipboardData)    {
           // the IE-manier
        window.clipboardData.setData("Text", text);
        success = true;
    }
    else if (window.netscape)  {
        if(netscape.security.PrivilegeManager != undefined) {
            netscape.security.PrivilegeManager.enablePrivilege('UniversalXPConnect');
            var clip = Components.classes['@mozilla.org/widget/clipboard;1'].getService(Components.interfaces.nsIClipboard);
            var trans = Components.classes['@mozilla.org/widget/transferable;1'].createInstance(Components.interfaces.nsITransferable);
            if(typeof(clip) == "object" && typeof(trans) == "object") {
                trans.addDataFlavor('text/unicode');
                var stingSupporter = Components.classes["@mozilla.org/supports-string;1"].createInstance(Components.interfaces.nsISupportsString);
                stingSupporter.data = text;
                trans.setTransferData("text/unicode", stingSupporter, text.length * 2);
                var clipid = Components.interfaces.nsIClipboard;
                clip.setData(trans, null, clipid.kGlobalClipboard);
                success = true;
            }
        }
        else { // Firefox > v15
            // Create Data URL
            if(fallbackContentType == undefined) fallbackContentType = "text/plain";
            var url = "data:"+ fallbackContentType +"," + encodeURIComponent(text);
            window.open(url);
        }
    }
    return success;
}