When you are applying to many of the marketing and branding grad schemes, the standard task they will get you to do, is write about a brand you love or hate, a brand you think could improve, or a brand that needs to reinvent itself etc.
It is a good idea to think long and hard about the example you use in order to distinguish youself from other candidates and show you actually have a genuine interest in this particular aspect of business.
1) Have a look at this article on brandchannel.com entilted 'What Makes a Great Brand?' Although, it is from a few years ago now, it is still a useful introduction to how to go about thinking about these case studies, as it talks (indirectly) about the key issues involved and addresses the specific points you might want to make. In all of this it is important not forget to about the strategic and business implications of your chosen brand.
2) If you are stuck for ideas, go to the Superbrands website and have a play about. Just click on one of the options on the left hand side (Superbrands, Coolbrands, Business Superbrands, eSuperbrands, Sport Brandleaders and Kids Superbrand). This will open up a website dedicated to each of the categories, with loads of examples and detail in the 'brand case studies' section, to which you can add your own personal analysis and viewpoints.