Apps purchased from the app store and songs purchased from iTunes can be downloaded again by going to the purchased section in the respective app and clicking the cloud button.
Neither app shows the audio-books I have purchased and when I look at a specific book I have already purchased in the iTunes store it shows the buy button.
Will I get charged again if I click the buy button or will it just re-download it?
Best Answer
Google shows various links that say that it is not possible to automatically re-download Audio Books in iTunes.
For example, this recent one - previously purchased audiobooks not showing up - from 3-Nov-2011:
Similarly:
A few replies, like this one, include extra info:
Conclusion
If you have any past back-ups of your desktop machine where you run iTunes and sync(ed) your device, you should be able to restore your purchase.
Otherwise, your best bet is to contact iTunes Store support.