The Qur'an:
Qur'an (5:51) - "O you who believe! do not take the Jews and the Christians for friends; they are friends of each other; and whoever amongst you takes them for a friend, then surely he is one of them; surely Allah does not guide the unjust people."
Qur'an (5:80) - "You will see many of them befriending those who disbelieve; certainly evil is that which their souls have sent before for them, that Allah became displeased with them and in chastisement shall they abide." Those Muslims who befriend unbelievers will abide in hell.
Qur'an (3:28) - "Let not the believers Take for friends or helpers Unbelievers rather than believers: if any do that, in nothing will there be help from Allah: except by way of precaution, that ye may Guard yourselves from them..." This last part means that the Muslim is allowed to feign friendship if it is of benefit. Renowned scholar Ibn Kathir states that "believers are allowed to show friendship outwardly, but never inwardly."
Qur'an (3:118) - "O you who believe! do not take for intimate friends from among others than your own people, they do not fall short of inflicting loss upon you; they love what distresses you; vehement hatred has already appeared from out of their mouths, and what their breasts conceal is greater still; indeed, We have made the communications clear to you, if you will understand." This verse not only warns Muslims not to take non-Muslims as friends, but it establishes the deep-seated paranoia that the rest of the world is out to get them.
Qur'an (9:23) - "O ye who believe! Choose not your fathers nor your brethren for friends if they take pleasure in disbelief rather than faith. Whoso of you taketh them for friends, such are wrong-doers" Even family members are not to be taken as friends if they do not accept Islam. (This is the mildest interpretation of this verse from the 9th Sura, which also advocates "slaying the unbeliever wherever ye find them").
Qur'an (53:29) - "Therefore shun those who turn away from Our Message and desire nothing but the life of this world."
Qur'an (3:85) - "And whoever desires a religion other than Islam, it shall not be accepted from him, and in the hereafter he shall be one of the losers."
Qur'an (3:10) - "(As for) those who disbelieve, surely neither their wealth nor their children shall avail them in the least against Allah, and these it is who are the fuel of the fire." Those who do not believe in Muhammad are but fuel for the fire of Hell (also 66:6, 2:24. 21:98).
Qur'an (7:44) - "The Companions of the Garden will call out to the Companions of the Fire: "We have indeed found the promises of our Lord to us true: Have you also found Your Lord's promises true?" They shall say, "Yes"; but a crier shall proclaim between them: "The curse of Allah is on the wrong-doers" Muslims in heaven will amuse themselves by looking down on non-Muslims in Hell and mocking them while they are being tortured (see 22:19-22.
Qur'an (1:5-7) - "Show us the straight path, The path of those whom Thou hast favoured; Not the (path) of those who earn Thine anger nor of those who go astray" This is a prayer that Muslims are supposed to repeat each day. "Those who earn Thine anger" specifically refers to Jews and "those who go astray" refers to Christians (see Bukhari (12:749)).
From the Hadith:
Muslim (1:417) - Taken to mean that one's own relatives should not be taken as friends if they are not Muslim.
Abu Dawud (41:4815) - "The Prophet (peace be upon him) said: A man follows the religion of his friend; so each one should consider whom he makes his friend."
Abu Dawud (41:4832) - The Messenger of Allah [said] "Do not keep company with anyone but a believer and do not let anyone eat your food but one who is pious."
Bukhari (59:572) - "O you who believe! Take not my enemies And your enemies as friends offering them (Your) love even though they have disbelieved in that Truth (i.e. Allah, Prophet Muhammad and this Quran) which has come to you."
Ishaq 262 - "Some Muslims remained friends with the Jews, so Allah sent down a Qur'an forbidding them to take Jews as friends. From their mouths hatred has already shown itself and what they conceal is worse"
Ishaq 252 - The story of a young man who converts to Islam after hearing Muhammad. He then tells his own father that he can no longer have anything to do with him because, "I have become a Muslim and follow the religion of Muhammad." (To maintain a relationship with his son, the father "converts" as well). This is an important passage because it establishes that the principle of shunning is based merely on the status of non-Muslims as unbelievers, not on their relations toward Muslims. In this case, the father desperately loved his son and meant him no harm.
Additional Notes:
Cultural superiority is a doctrine of Islam that actually has a name; it's called Jahiliyya - and literally means that any culture without Islam is "ignorant and stupid." Stunning bigotry by Islamic scholars is so casual that it often goes unnoticed. For example, a 2007 fatwa responds to a question on whether Muslims can swim in a pool in which a non-Muslim has swam:
If the size of the public pool is more than 225 sq ft (20.9 m2) then it is considered a large body of water and will not become impure by non-Muslims swimming in it. If the pool is less then 225 sq ft (20.9 m2), then if the non-Muslim had taken a bath before swimming, the water will be pure since there is no impurity on him. If he did not take a bath before swimming and it is certain that there was impurity on him before he swam, then the pool is impure and all the water must be removed and refilled with clean water.
Even though they are explicitly kufr (unbelievers, Qur'an 5:17, 4:44-59) Jews and Christians are given special status in the Quran. So, if Muhammad warned believers against taking them as friends, then it surely is not permissible for Muslims to befriend atheists or those of other religions.
Some Muslims interpret this to mean that they should not even act friendly toward nonbelievers; fortunately, many do not. Islamic TV preacher Sheikh Muhammad Hassan says that a Muslim is not even permitted to smile at a non-Muslim. A fatwa from Islam Q&A, permits infidels to be dealt with "in a kind manner in the hope that they might become Muslim," but it warns Muslims against taking unbelievers as "sincere friends" (The same site also encourages Muslims to "stop keeping company with Christians and replace them with Muslim friends").
The book, al-Wala' wa'l-Bara' by Shaykh Muhammad Saeed al-Qahtani, lists 20 "types of alliances" with unbelievers that are forbidden to Muslims. These include "taking the disbelievers as friends," "trusting the disbelievers," "drawing near" to them and even living among them.
Some Muslims are embarrassed by verse 5:51 and have gone to elaborate lengths to modify its intent by interpreting the word 'friend' as "guardian" or "protector" - which are just two of several legitimate translations of the Arabic word. According to these apologists, the verse is referring to a Muslim's allegiance to a non-Muslim government (which is not all that comforting either).
However, the word awliyaa is used in verse 5:51 instead of other words that would be more direct if the meaning were "protector" - such as hamin. In fact, the politically correct translations that do use the word "protector" turn right around and use the word "friend" in other places for the same Arabic word - such as in verse 10:62.
In fact, it is verse 10:62 which proves that the word awliyaa truly means "friend" in the Quran and not "guardian" because it refers to associates of Allah (translated "friends of Allah"). If the word meant "guardian" then it would mean that Allah has guardians, which is blasphemy.
Apologists sometimes point to verse 60:8-9 which says that Allah doesn't necessarily forbid showing kindness to unbelievers, but to shun the ones "who warred against you on account of religion and have driven you out from your homes and helped to drive you out." This is an obvious reference to the Meccans, whose leaders expelled Muhammad and his handful of followers from Mecca (following his declaration of war against them). The verse was narrated shortly after their arrival in Medina, when it was necessary for the numerically disadvantaged Muslims to build alliances with non-Muslims in order to survive. The verses quoted above from Suras 9 and 5 are narrated at a later time and under much different circumstances, when Muslims had power. The verses expand the scope of unfriendliness to include anyone who is not Muslim.
Modern apologists such as Jamal Badawi try to cloud the straightforward interpretation of verse 5:51 by pointing out that Muslims are allowed to take non-Muslims as marriage partners, thus implying friendship. In truth, verse 2:221 explicitly forbids Muslims from marrying unbelievers, even though verse 5:5 allows it (Allah's change of mind corresponded somewhat curiously with Muhammad's own desire to marry a non-Muslim woman). Yusuf Ali reconciles the contradiction by saying that non-Muslims wives are "expected" to become Muslim.
In any event, only Muslim men are allowed to marry outside the faith. The women they marry relinquish control over their own lives, even to the extent that they cannot teach their faith to their own children, who must be raised Muslim. The non-Muslim woman also agrees to a lifetime of sexual servitude, and may be beaten if she does not submit.
This certainly doesn't sound like friendship to the rest of us. Moreover, if 'interfaith' marriage is about friendship between peers and not domination, then why are Muslim women banned from marrying non-Muslim men?
On the whole, Islam is very clear in teaching that there is no equality between believers and unbelievers, and hence no basis for friendship, which is a relationship between peers.