With UX being a young discipline, it's still hard to know what the required readings are (and in fact where there are readings aside from blog posts). However, a number of people have created compilations of appropriate books. Here they are:
If you're looking for a place to start, look no further than the list by Adaptive Path. This compilation includes a number of seminary texts (it doesn't hurt that a lot of them are ex-Adaptive Path employees), with comments on each book.
I want to read it … now!
The title is a misomer as not all of the books are free, but for this list is valuable for Jennifer Tidwell's 'Designing Interaces' alone.
Everything and the kitchen sink
Will Evans and Dave Malouf have created a comprehensive list of UX texts. The sheer size of it (and the lack of comments) does not make it for the faint hearted, but for those who know their Search Interfaces from Social Web will appreciate this text to check what they have and haven't read.
Before IXDA …
Interesting compilation of texts from the beginning of computing/HCI.
You say service, I say experience
A companion list for Eric Reiss's UX London talk, these books are an insight into the customer end of experience, with detailed explanation of their relevance.
Get up with the lingo
This list is more academic than pragmatic (think Klaus Krippendorf rather than Tom Peters), and unannnotated, but interesting for those looking to deepen their knowledge on design thinking.
For those looking for variety
A wonderfully eclectic annotated biography, ranging from phenomenology to Arduino. Great list for those looking for a range.