For quite a few of the essay courses at Cambridge, there are opportunities to work on a dissertation. This would normally be in the later years, and sometimes you can choose to write a dissertation to replace one of your exam papers (see the structure of your chosen course). As Fiona, one of our History students says, 'it’s a good way to spend time studying something that you’re particularly interested in, and to research material which has hardly been studied before'. Many students enjoy researching and writing their dissertation so much that they decide to go on to further research after their degree, and they apply for Masters and PhD courses.
Christ's College has produced a very interesting resource with accounts of what some current undergraduates are studying for their dissertations. Do visit their website to find out more: