Are there any verses in the Koran that really states women should cover their heads?

There are not any verses. The idea of covering up is just being used by some people/governments to force their views on others & to control. If Muslims understood their religion better, they would know better. Islam talks about modesty- just as christianity does. Let God be the judge.

Peace

to understand islam u need to understand quran and hadith. U cannot understand islam by just the quran. Since the study of the quran is a science of its own.

In my little knowlegde it is mentioned about the covering of the all except the face and the hands. I don't have exact verse.

Sura 24:31 31.And tell the believing women to subdue their eyes, and maintain their chastity. They shall not reveal any parts of their bodies, except that which is necessary. They shall cover their chests, and shall not relax this code in the presence of other than their husbands, their fathers, the fathers of their husbands, their sons, the sons of their husbands, their brothers, the sons of their brothers, the sons of their sisters, other women, the male servants or employees whose sexual drive has been nullified, or the children who have not reached puberty. They shall not strike their feet when they walk in order to shake and reveal certain details of their bodies. All of you shall repent to GOD, O you believers, that you may succeed.*

Sura 33:55 55. The women may relax (their dress code) around their fathers, their sons, their brothers, the sons of their brothers, the sons of their sisters, the other women, and their (female) servants. They shall reverence GOD. GOD witnesses all things.

Sura 33:59 59. O prophet, tell your wives, your daughters, and the wives of the believers that they shall lengthen their garments. Thus, they will be recognized (as righteous women) and avoid being insulted. GOD is Forgiver, Most Merciful.

Sura 24:60 60. The elderly women who do not expect to get married commit nothing wrong by relaxing their dress code, provided they do not reveal too much of their bodies. To maintain modesty is better for them. GOD is Hearer, Knower.

In Sorat Al-Noor, chapter 24, verse 31:

(30) And tell the believing women to lower their gaze and be modest, and to display of their adornment only that which is apparent, and to draw their veils over their bosoms, and not to reveal their adornment save to their own husbands or fathers or husbands' fathers, or their sons or their husbands' sons, or their brothers or their brothers' sons or sisters' sons, or their women, or their slaves, or male attendants who lack vigour, or children who know naught of women's nakedness. And let them not stamp their feet so as to reveal what they hide of their adornment. And turn unto Allah together, O believers, in order that ye may succeed. (31)