Quran (4:11) - (Inheritance) "The male shall have the equal of the portion of two females" (see also verse 4:176). In Islam, sexism is mathematically established.
Quran (2:282) - (Court testimony) "And call to witness, from among your men, two witnesses. And if two men be not found then a man and two women." Muslim apologists offer creative explanations to explain why Allah felt that a man's testimony in court should be valued twice as highly as a woman's, but studies consistently show that women are actually less likely to tell lies than men, meaning that they make more reliable witnesses.
Quran (2:228) - "and the men are a degree above them [women]"
Quran (5:6) - "And if ye are unclean, purify yourselves. And if ye are sick or on a journey, or one of you cometh from the closet, or ye have had contact with women, and ye find not water, then go to clean, high ground and rub your faces and your hands with some of it" Men are to rub dirt or water on their hands to purify themselves, following casual contact with a woman (such as shaking hands).
Quran (24:31) - Women are to lower their gaze around men, so they do not look them in the eye. (To be fair, men are told to do the same thing in the prior verse).
Quran (2:223) - "Your wives are as a tilth unto you; so approach your tilth when or how ye will..."A man has dominion over his wives' bodies as he does his land. This verse is overtly sexual. There is some dispute as to whether it is referring to the practice of anal intercourse. If this is what Muhammad meant, then it would appear to contradict what he said in Muslim (8:3365).
Quran (4:3) - (Wife-to-husband ratio) "Marry women of your choice, Two or three or four" Inequality by numbers.
Quran (53:27) - "Those who believe not in the Hereafter, name the angels with female names." Angels are sublime beings, and would therefore be male.
Quran (4:24) and Quran (33:50) - A man is permitted to take women as sex slaves outside of marriage. Note that the verse distinguishes wives from captives (those whom they right hand possesses).
Hadith and Sira
Sahih Bukhari (6:301) - "[Muhammad] said, 'Is not the evidence of two women equal to the witness of one man?' They replied in the affirmative. He said, 'This is the deficiency in her intelligence.'"

Sahih Bukhari (6:301) - continued - "[Muhammad said] 'Isn't it true that a woman can neither pray nor fast during her menses?' The women replied in the affirmative. He said, 'This is the deficiency in her religion.'" Allah has made women deficient in the practice of their religion as well, by giving them menstrual cycles.

Sahih Bukhari (2:28) & Sahih Bukhari (54:464) - Women comprise the majority of Hell's occupants. This is important because the only women in heaven mentioned explicitly by Muhammad are the virgins who serve the sexual desires of men. (A weak Hadith, Kanz al-`ummal, 22:10, even suggests that 99% of women go to Hell).

Sahih Bukhari (62:81) - "The Prophet said: "'The stipulations most entitled to be abided by are those with which you are given the right to enjoy the (women's) private parts (i.e. the stipulations of the marriage contract).'" In other words, the most important thing a woman brings to marriage is between her legs.

Sahih Bukhari (62:58) - A woman presents herself in marriage to Muhammad, but he does not find her attractive, so he "donates" her on the spot to another man.

Sahih Muslim (4:1039) - "A'isha said [to Muhammad]: 'You have made us equal to the dogs and the asses'" These are the words of Muhammad's favorite wife, complaining of the role assigned to women under Islam.

Abu Dawud (2:704) - "...the Apostle of Allah (peace_be_upon_him) said: When one of you prays without a sutrah, a dog, an ass, a pig, a Jew, a Magian, and a woman cut off his prayer, but it will suffice if they pass in front of him at a distance of over a stone's throw."

Abu Dawud (2155) - Women are compared to slaves and camels with regard to the "evil" in them.

Ishaq 734 - "As for Ali, he said, 'Women are plentiful, and you can easily change one for another.'"Ali was raised as a son by Muhammad. He was also the 4th caliph. This comment was made in Muhammad's presence without a word of rebuke from him.

Ishaq 878 - "From the captives of Hunayn, Allah's Messenger gave [his son-in-law] Ali a slave girl called Rayta and he gave [future Caliph] Uthman a slave girl called Zaynab and [future Caliph] Umar a girl to whom Umar gave to his son." - Even in this world, Muhammad treated women like party favors, handing out enslaved women to his cronies for sex.

Ibn Ishaq 693 - "Then the apostle sent Sa-d b. Zayd al-Ansari, brother of Abdu'l-Ashal with some of the captive women of Banu Qurayza to Najd and he sold them for horses and weapons." Muhammad traded captured women for horses.

Al-Tirmidhi 3272 - "When Allah's Messenger was asked which woman was best he replied, 'The one who pleases (her husband) when he looks at her, obeys him when he gives a command, and does not go against his wishes regarding her person or property by doing anything of which he disapproves'." (See also Abu Dawud 1664)

Tabari 8:117 - The fate of more captured farm wives, whom the Muslims distributed amongst themselves as sex slaves: "Dihyah had asked the Messenger for Safiyah when the Prophet chose her for himself... the Apostle traded for Safiyah by giving Dihyah her two cousins. The women of Khaybar were distributed among the Muslims."

Tabari 9:137 - "Allah granted Rayhana of the Qurayza to Muhammad as booty."

Ishaq 969 - "Lay injunctions on women kindly, for they are prisoners with you having no control of their persons." - This same text also says that wives may be beaten for "unseemliness".

Tabari 9:1754 - "Treat women well, for they are [like] domestic animals with you and do not possess anything for themselves." From Muhammad's 'Farewell Sermon'.
Notes
The move to paint Islam as a pioneering force in women's rights is a recent one, corresponding with the efforts of Muslim apologists (not otherwise known for their feminist leanings) and some Western academics prone to interpreting history according to personal preference. In truth, the Islamic religious community has never exhibited an interest in expanding opportunities for women beyond the family role.

The fourth Caliph, who was Muhammad's son-in-law and cousin, said just a few years after the prophet's death that "The entire woman is an evil. And what is worse is that it is a necessary evil."

A traditional Islamic saying is that, "A woman's heaven is beneath her husband's feet." One of the world's most respected Quran commentaries explains that, "Women are like cows, horses, and camels, for all are ridden." (Tafsir al-Qurtubi)

The revered Islamic scholar, al-Ghazali, who has been called 'the greatest Muslim after Muhammad,' writes that the role of a Muslim woman is to "stay at home and get on with her sewing. She should not go out often, she must not be well-informed, nor must she be communicative with her neighbors and only visit them when absolutely necessary; she should take care of her husband... and seek to satisfy him in everything... Her sole worry should be her virtue... She should be clean and ready to satisfy her husband's sexual needs at any moment." [Ibn Warraq]

A Yemeni cleric recently explained in a television broadcast what makes women inferior and unable, say, to serve as good witnesses: "Women are subject to menstruation, when their endurance and mental capacity for concentration are diminished. When a woman witnesses a killing or an accident, she becomes frightened, moves away, and sometimes even faints, and she cannot even watch the incident."

During a 2012 talk show on an Egyptian television channel, a cleric slammed Christianity - in part for teaching gender equality: “the Christian religion does not differentiate between women and men, but it confirms their perfect equality: it gives them an equal share in inheritance, it bans divorce, and it bans polygamy.”

In 2014, Turkish President Recep Tayyip Erdogan emphasized that men and women are not equal: "Our religion has defined a position for women (in society): motherhood."

Linda Sarsour, a hijab-clad Sharia proponent who also bills herself as a 'feminist' said of a real feminist, Ayaan Hirsi Ali, that she should have her vagina removed for opposing Islam. The remarks were particularly hateful given that Hirsi Ali is a survivor of female genital mutilation.

The many opportunities denied women under Islamic law, from equal testimony in court to the simple right to exclude other wives from their marital bed, is very clear proof that women are of lesser value then men in Islam. Muslim women are not even free to marry outside the faith - and some pay with their lives for doing so.

Islamic law also specifies that when a woman is murdered by a man, her family is owed only half as much "blood money" (diya) as they would be if she had been a man. (The life of a non-Muslim is generally assessed at one-third).

Although a man retains custody of his children in the event of his wife's death, a non-Muslim woman will automatically lose custody of her children in the event of her husband's death unless she converts to Islam or marries a male relative within his family.

Contemporary Muslims like to counter that Arabs treated women as camels prior to Muhammad. This is somewhat questionable, given that Muhammad's first wife was a wealthy woman who owned property and ran a successful business prior to ever meeting him. She was even his boss... (although that may have changed after the marriage). Still, it is somewhat telling that Islam's treatment of women can only be defended by contrasting it to an extremely primitive environment in which women were said to be non-entities.

Homa Darabi was a talented physician who took her own life by setting herself on fire in a public protest against the oppression of women in Islamic Iran. She did this after a 16-year-old girl was shot to death for wearing lipstick. In the book, Why We Left Islam, her sister includes a direct quote from one of the country's leading clerics:

"The specific task of women in this society is to marry and bear children. They will be discouraged from entering legislative, judicial, or whatever careers which may require decision-making, as women lack the intellectual ability and discerning judgment required for these careers."

Modern day cleric Abu Ishaq al-Huwaini has called for a return of the slave markets, where Muslim men can order concubines. In this man's ideal world, "when I want a sex-slave, I go to the market and pick whichever female I desire and buy her."

At best, Islam "elevates" the status of a woman to somewhere between that of a camel and a man. Muhammad captured women in war and treated them as a tradable commodity. The "immutable, ever-relevant" Quran explicitly permits women to be kept as sex slaves. These are hardly things in which Muslims can take pride.