I'm a computational PhD student in the field -- I think you'd most enjoy "On Intelligence" by Jeff Hawkins, an inspiring book written by a hacker himself!

If you'd like a very excellent, fascinating title on mathematics and art and mind, try "Godel, Escher, Bach" by Hofstadter. Another fun, classical book with more of an AI bend is "Society of Mind" by Marvin Minsky.

For more classical neuroscience, "Phantoms of the Brain" by Ramachandran, well-known in perception research, is good. I haven't read it, but "In Search of Memory" is supposed to be excellent by Kandel, a memory researcher superstar. (I've found that many of the books by non-scientists about the brain are often shallow, claim to know too much, and use the same familiar stories over and over.) For neuroscience at a lower level (i.e. the biology of neurons, neural networks, cells), I'm not aware of a good popular account.

I also recommend picking up a copy of Mind magazine from your bookstore! And if you can get a copy of a Scientific American magazine special on the brain (every few years I believe), those are usually very well written as well :-)