JQuery :: Use CSS Selectors That Are Not Defined In A Stylesheet?

Is it common to use CSS selectors that are not defined in a stylesheet (or anywhere else) to identify HTML elements? When using jQuery in ASP.Net with controls that implement INamingContainer, all it's children's ID's are automatically generated based on the id of the child control and the id of the container control (such as the Panel control) so we couldn't simply use $("#myChildControl") for a child control with the id of 'myChildControl'. The resulting client id would be something like 'mypanel_mychildcontrol' and for autogenerated controls within grids/tables, the id's get even more complicated and should be 'guessed'. So, how does/would people identify these types of controls when there are no preset CSS selector's for them?

On the server side, we can use the ClientID to get the generated ID, but for some things, I just want to do this totally on the client side without messing with code-behind.