I joined the Oxford Council library soon after arrival in Oxford, but never found much to get excited by in their holdings, since they have neither academic books nor much in the way of world literature.
It wasn't till recently that I got around to getting a Bodleian readers card. This was very easy - I just turned up with the forms and paid my money - with the only unusual feature being that they made me speak the oath out loud!
The first book I looked for in the catalogue was The Development of Atmospheric Circulation Models. I couldn't find this, however, and an email query revealed that, being a copyright deposit library, the Bodleian doesn't actually buy copies of books published in the UK — and their official copy hadn't arrived yet. So there are drawbacks to your institution having a deposit library! Fortunately I managed to get a review copy of this from Cambridge University Press.
The second book I went looking for was volume 28 of The Collected Writings of John Maynard Keynes, because a group of friends has been debating how much Marx Keynes had read, on which a letter from him to Bernard Shaw looked like it might shed some light. The main Bodleian library has a copy of this, but when I put a Hold on that I got an email back saying that my request had been cancelled because the work was "being transferred to BSF Swindon". This volume is also held by some of the college libraries, but apparently getting access to those can be difficult even for members of the university... I will have to see if my sister can get me into the Christ Church library.
The third book I looked for was Zhou Ruchang's From Noble to Humble: Cao Xueqin and the Dream of the Red Chamber. This turned out to be in the Bodleian Chinese Studies Library, so that was the first of the libraries I visited. This is a nice modern room, with easy access to the collection and desks with convenient power sockets, so it will be quite a comfortable place to bring my laptop and write a review. (As an external reader I'm not allowed to actually borrow books.)
There was a petition on the front desk here opposing the closing of the library, so I suspect the Bodleian is going to do what Fisher library did at Sydney and close some of its smaller specialist libraries. Many of the libraries at Oxford University aren't part of the Bodleian, however, so there's a limit to how far this can go. The college libraries in particular are unlikely to be assimilated — apparently when everything was centrally catalogued some of the colleges didn't even want the world to know what they had.
The Cherwell magazine recently ran a story on Oxford's Lesser-Loved Libraries (hat tip Sophia) which will make a useful guide. I also have a recommendation for the American Studies library — from a plant biologist who could presumably be sure he wasn't going to be accosted there by students or colleagues.