I would recommend keeping your URL's as clean as possible and to try and use routes whenever possible. You should try and make RESTful URI's that will convey information to the user. For example:
www.yourdomain.com/Products/Sports/Clothing
is a lot cleaner than
www.yourdomain.com/Products?Department=Sports&SubDepartment=Clothing
If you use a ton of query strings then it won't be a clean URI and less information is conveyed to the user.
With that said, our team does use query strings for ajax type requests using jquery. This is because these URI's are in our markup and won't be seen in the browser window. This has helped keep our global.asax a little smaller since it won't get polluted with a ton of routes.