How can I make a function defined in jQuery.ready available globally?

You have two options, add it to the window object to make it global:

window.getList = function(url, gkey){ 
    // etc...
}

or move it from inside the document ready event handler into the global scope:

$(document).ready(function() {  
    alert(getList('http://www.youtube.com/watch?v=dm4J5dAUnR4', "v"));
});  
var getList = function(url, gkey){  

    var returned = null;  
    if (url.indexOf("?") != -1){  
      var list = url.split("?")[1].split("&"),  
              gets = [];  

      for (var ind in list){  
        var kv = list[ind].split("=");  
        if (kv.length>0)  
            gets[kv[0]] = kv[1];  
    }  

    returned = gets;  

    if (typeof gkey != "undefined")  
        if (typeof gets[gkey] != "undefined")  
            returned = gets[gkey];  

    }  

        return returned;  

};  

You might also want to read this question about using var functionName = function () {} vs function functionName() {}, and this article about variable scope.