I've read parts of it as a result of my religious (moderately religious) upbringing, parts of it I have read for religion, culture and philosophy classes, and parts of it I have read of my own interest.
But regardless of its legitimacy as a historical or philosophical text, there is no denying the sweeping influence it has had on western and some non-western civilizations for millenia. I think people should read a good deal of it in order to be culturally literate and informed about the nature of ideologies influencing many of our socio-political movements and conflicts in the world today.
You can probably skip kings, numbers, judges, ester, Isaiah, Joel, Jonas, Habbakuk, Obediah, Nahamuh, Nahum, Amos, and Hosea.
ETA: By the same token I should read the Koran, The magna carta, pax whatever, and orations...but I still have time.