The below code snippet explains how to get the Text and Value part of the Selected item of ASP.Net RadioButtonList using jQuery
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
    <title></title>
    <script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1.8.3/jquery.min.js"></script>
    <script type="text/javascript">
        $("#demo").live("click", function () {
            var selectedItem = $("[id*=RadioButtonList1] input:checked");
            if (selectedItem.length > 0) {
                alert("Selected Value: " + selectedItem.val() + " Selected Text: " + selectedItem.next().html());
            } else {
                alert("Please select an item.");
            }
        });
    </script>
</head>
<body>
    <form id="form1" runat="server">
    <asp:RadioButtonList ID="RadioButtonList1" runat="server">
        <asp:ListItem Text="One" Value="1" />
        <asp:ListItem Text="Two" Value="2" />
        <asp:ListItem Text="Three" Value="3" />
    </asp:RadioButtonList>
    <br />
    <input type = "button" id = "demo" value = "Demo" />
    </form>
</body>
</html>
 
 
Explanation:
In the above code snippet I have assigned a click event handler to the HTML input button with ID demo. When the button is clicked the selected item (radio button) of the ASP.Net RadioButtonList is fetched using the [id*=RadioButtonList1] input:checked  jQuery selector. If the length of the selected item is greater than zero the Value and the Text Part of the selected item of the ASP.Net RadioButtonList is displayed in JavaScript alert.
Demo: