O you who believe! Take not My enemies and your enemies (i.e. disbelievers and polytheists, etc.) as friends, showing affection towards them, while they have disbelieved in what has come to you of the truth (i.e. Islamic Monotheism, this Quran, and Muhammad SAW), and have driven out the Messenger (Muhammad SAW) and yourselves (from your homeland) because you believe in Allah your Lord! If you have come forth to strive in My Cause and to seek My Good Pleasure, (then take not these disbelievers and polytheists, etc., as your friends). You show friendship to them in secret, while I am All-Aware of what you conceal and what you reveal. And whosoever of you (Muslims) does that, then indeed he has gone (far) astray, (away) from the Straight Path. (Qur'an 60:1)
If they gain dominance over you, they would be to you as enemies and extend against you their hands and their tongues with evil, and they wish you would disbelieve. (Qur'an 60:2)
Indeed there has been an excellent example for you in Ibrahim (Abraham) and those with him, when they said to their people: "Verily, we are free from you and whatever you worship besides Allah, we have rejected you, and there has started between us and you, hostility and hatred for ever, until you believe in Allah Alone," except the saying of Ibrahim (Abraham) to his father: "Verily, I will ask for forgiveness (from Allah) for you, but I have no power to do anything for you before Allah." Our Lord! In You (Alone) we put our trust, and to You (Alone) we turn in repentance, and to You (Alone) is (our) final Return, (Qur'an 60:4)
"Our Lord! Make us not a prey for those who disbelieve, and forgive us, our Lord! Lo! Thou, only Thou, are the Mighty, the Wise. (Qur'an 60:5)
Certainly, there has been in them an excellent example for you to follow, for those who look forward to (the Meeting with) Allah (for the reward from Him) and the Last Day. And whosoever turn away, then verily, Allah is Rich (Free of all wants), Worthy of all Praise. (Qur'an 60:6)
Perhaps Allah will make friendship between you and those whom you hold as enemies. And Allah has power (over all things), and Allah is Oft-Forgiving, Most Merciful. (Qur'an 60:7)
Allah does not forbid you to deal justly and kindly with those who fought not against you on account of religion and did not drive you out of your homes. Verily, Allah loves those who deal with equity. (Qur'an 60:8)
It is only as regards those who fought against you on account of religion, and have driven you out of your homes, and helped to drive you out, that Allah forbids you to befriend them. And whosoever will befriend them, then such are the Zalimun (wrong-doers those who disobey Allah). (Qur'an 60:9)
I apologize for the big answer, but to get a complete picture you have to read that all.
This is chapter no. 60 (Surat Al-Mumtahanah), I think **these verses are the abrogated ones over any precious verses. **
friend = a person whom one knows and with whom one has a bond of mutual affection (Oxford Dictionary)
So, we need to capture what's going on in the above verses. Firstly, Allah said to befriend (Non -Believers) then he is telling we might become friends, and then he says, do not befriend those who've fought not against you or the Prophet(pbuh). But, he doesn't say make friends with the disbelievers, but he says, deal with them justly. So, the example of Ibrahim (pbuh) mentioned above applies, and Allah says, do not make them your close friends. Because their negative behavior is very likely to influence you.
O you who believe! Take not as friends the people who incurred the Wrath of Allah (i.e. the Jews). Surely, they have been in despair to receive any good in the Hereafter, just as the disbelievers have been in despair about those (buried) in graves (that they will not be resurrected on the Day of Resurrection). (Qur'an 60:13)
May the creator guide us all.