The general consensus is that you can read Qur'an for your deceased relatives as long as they died on Islam, because of the Hadeeth, "When a man dies, his acts come to an end, but three, recurring charity, or knowledge (by which people) benefit, or a pious son, who prays for him (for the deceased)." This means that reading Qur'an for the deceased will benefit them in their graves; it is even advised to do so.
However, reading Qur'an for deceased infidels is prohibited explicitly in the Qur'an. Allah said, "It is not for the Prophet and those who have believed to ask forgiveness for the polytheists, even if they were relatives, after it has become clear to them that they are companions of Hellfire." (Al-Tawbah, verse :113).
Edit: After reviewing more recent literature (especially fatwas of Sheikh Attia Sakr of Al Azhar's Fatwa Committee), I can say that even reading Qur'an (and asking forgiveness generally) for deceased non-Muslims has some controversy around it. The idea that many have received a distorted picture of Islam, opens up for the case of people of the interval between Prophet Jesus, and Prophet Mohammad. The idea is basically, those whom the message hasn't reached (or reached in bad, distorted form for our case) will have the chance in the Judgement Day to join Islam. For this matter, asking forgiveness for deceased non-Muslims can help them in the afterlife.
-Hadeeth from Sahih Moslem, Book of Wills.
-The verse is form Surat Al-Tawbah.
-See Majmoo'e Ftawa Al-Akeeda for Sheikh Ibn Othaimain, Vol.2 p.305
-For Sheikh Attia Sakr Fatwa, check his book Al-Fatawa, Al-Tawfikia Press, pp.31,33 and pp.315,319