Whilst some geography courses will ask that certain books be bought, there are some which are really useful on any course and so are worth buying asap. Especially for first year there will be some key text books that cover certain areas of the course that are useful to buy because you will use them a lot, and they will be hot property in the university libraries.
Fundamentals of the Physical Environment. Smithson, Addison and Atkinson
There are many versions of this classic physical geography textbook. The book is clear, well organised and contains lots of pictures and diagrams as any good geography book should. A newer edition is probably better, given the volume of new research produced by physical geographers.
Statistics for Geography and Environmental Sciences. Harris and Jarvis
Increasingly geographers are needing to have a good understanding of statistics in order to carry out good research. Therefore university departments are incorporating statistics into geographical methodology parts of geography degrees. This book explains statistics and the use of them in geography very well, mainly due to the use of simple examples. This book will really help you make sense of statistics in geography, sometimes however departments may only have two or three copies, so it's a good investment.
Useful pre-course reading
If you want to get a head start in your studies, get a better idea of what you will be learning about and just want to give yourself some piece of mind, then doing a bit of pre-course reading is a really great idea. Reading fairly introductory geography books and articles is the best idea, and will provide lots of ideas and themes for you to develop once at university. This list names books that students read or wished they had read before starting.
Introducing Human Geographies. Cloke, Crang, Goodwin.
The best introduction to human geography this author has come across. Whilst more experienced students may say that this book isn't really useful in later work, it gives students a fantastic insight into how human geography is studied, what issues it explores and in what theoretical ways. This book is well worth buying, again the newer edition is your best bet. Key areas to read: Society-space, Culture-nature, Image-reality, Imaginative Geographies, Money and Finance. Also just take a pick from what catches your eye in the contents, it's all great stuff!