Edit: mis-read your original question - updating this answer accordingly.
ASP.NET renders the checkBoxList control to be a series of checkboxes (you can use firebug to easily see the rendered controls). I believe it assigns the ID of each checkbox, based on the ID you specified. For example:
<asp:CheckBoxList id="list1" runat="server">
<asp:ListItem>One</asp:ListItem>
<asp:ListItem>Two</asp:ListItem>
<asp:ListItem>Three</asp:ListItem>
</asp:CheckBoxList>
Is rendered in HTML as:
<table id="list1">
<tr><td><input id="list1_0" type="checkbox" /><label for="list1_0">One</label></td></tr>
<tr><td><input id="list1_1" type="checkbox" /><label for="list1_1">Two</label></td></tr>
<tr><td><input id="list1_2" type="checkbox" /><label for="list1_2">Three</label></td></tr>
</table>
You can determine if a box is checked via:
$('#list1_0').attr('checked')
You can also find them all via:
$('#list1 input')
... then use jQuery iteration to scan through all checkboxes. I suspect jQuery can also be used to find the next "label" control after a target checkbox control, and extract the actual text from it. One of stackoverflow's bigger jQuery brains will have to help with with the exact selector syntax - I'm relatively new to jQuery, and don't know it off the top of my head.
Original response (applies to simple selectionLists):
This should get the selected index:
$("#SomeListID").attr("selectedIndex")
This should get the selected value:
$("#SomeListID").val()