Allah says in the Holy Quran,

يٰۤاَيُّهَا الَّذِيْنَ اٰمَنُوْا لَا تَتَّخِذُوا الْيَهُوْدَ وَالنَّصٰرٰۤي اَوْلِيَآءَ ؔۘ بَعْضُهُمْ اَوْلِيَآءُ بَعْضٍ وَمَنْ يَّتَوَلَّهُمْ مِّنْكُمْ فَاِنَّهٗ مِنْهُمْ اِنَّ اللهَ لَا يَهْدِي الْقَوْمَ الظّٰلِمِيْنَ.

O you who believe, do not take the Jews and the Christians for intimate friends. They are friends to each other. Whoever takes them as intimate friends is one of them. Surely, Allah does not take the unjust people to the right path.. Sura Ma'idah, Verse 51

On the other hand, He said to Muslims,

وَالْمُؤْمِنُوْنَ وَالْمُؤْمِنٰتُ بَعْضُهُمْ اَوْلِيَآءُ بَعْضٍ يَاْمُرُوْنَ بِالْمَعْرُوْفِ وَيَنْهَوْنَ عَنِ الْمُنْكَرِ وَيُقِيْمُوْنَ الصَّلٰوةَ وَيُؤْتُوْنَ الزَّكٰوةَ وَيُطِيْعُوْنَ اللهَ وَرَسُوْلَهٗ اُولٰٓىِٕكَ سَيَرْحَمُهُمُ اللهُ اِنَّ اللهَ عَزِيْزٌ حَكِيْمٌ

The believers, male and female, are friends to each other. They bid virtue and forbid vice and establish Salah and pay Zakah and obey Allah and His Messenger. Those are the ones whom Allah will bless with mercy. Surely, Allah is Powerful, Wise. Sura Tawbah, Verse71

In another verse, He said,  

يٰۤاَيُّهَا الَّذِيْنَ اٰمَنُوْا لَا تَتَّخِذُوا الْكٰفِرِيْنَ اَوْلِيَآءَ مِنْ دُوْنِ الْمُؤْمِنِيْنَ اَتُرِيْدُوْنَ اَنْ تَجْعَلُوْا لِلهِ عَلَيْكُمْ سُلْطٰنًا مُّبِيْنًا.

O you who believe, do not take the disbelievers for friends instead of the believers. Do you want to produce before Allah a clear evidence against yourselves? Sura Nisa, Verse144

It is ordered to avoid not only disbelievers but also those who maintain relations with disbelievers and prefer disbelief over faith. Muslims must avoid them even if they are their fathers or brothers. Allah said,

يٰۤاَيُّهَا الَّذِيْنَ اٰمَنُوْا لَا تَتَّخِذُوْۤا اٰبَآءَكُمْ وَاِخْوَانَكُمْ اَوْلِيَآءَ اِنِ اسْتَحَبُّوا الْكُفْرَ عَلَي الْاِيْمَانِ وَمَنْ يَّتَوَلَّهُمْ مِّنْكُمْ فَاُولٰٓىِٕكَ هُمُ الظّٰلِمُوْنَ.

O you who believe, do not take your fathers and your brothers as your friends, if they prefer infidelity to Faith. Those of you who have friendship with them are the wrongdoers. Sura Tawbah, Verse 23

In the same way, it is ordered to avoid those we cause harm to Muslims, feel happy when Muslims are in difficulties. Allah said,

يٰۤاَيُّهَا الَّذِيْنَ اٰمَنُوْا لَا تَتَّخِذُوْا بِطَانَةً مِّنْ دُوْنِكُمْ لَا يَاْلُوْنَكُمْ خَبَالًا وَدُّوْا مَا عَنِتُّمْ  قَدْ بَدَتِ الْبَغْضَآءُ مِنْ اَفْوَاهِهِمْ  وَمَا تُخْفِيْ صُدُوْرُهُمْ اَكْبَرُ قَدْ بَيَّنَّا لَكُمُ الْاٰيٰتِ اِنْ كُنْتُمْ تَعْقِلُوْنَ.

O you who believe, do not take anyone as an insider but those from among your own selves. They would spare no effort to do you mischief. They want you to be in trouble. Malice has come out of their mouths while what is concealed in their hearts is still worse. We have made the signs clear to you, if only you understand. Sura Alu 'imran, Verse, 118

It is clearly said in a verse that the Jews and the mushriks ( those who ascribe partners to Allah) are the staunchest enemies of Muslims.

لَتَجِدَنَّ اَشَدَّ النَّاسِ عَدَاوَةً لِّلَّذِيْنَ اٰمَنُوا الْيَهُوْدَ وَالَّذِيْنَ اَشْرَكُوْا.

And you will certainly find that the people most hostile against the believers are the Jews and the ones who ascribe partners to Allah. Sura Ma'idah, Verse 82

It is a great blessing for a Muslim that Allah announced them as His friends.

اِنَّمَا وَلِيُّكُمُ اللهُ وَرَسُوْلُهٗ وَالَّذِيْنَ اٰمَنُوا الَّذِيْنَ يُقِيْمُوْنَ الصَّلٰوةَ وَيُؤْتُوْنَ الزَّكٰوةَ وَهُمْ رٰكِعُوْنَ.

Your only friend is Allah, then His Messenger and those who believe, who establish Salah and pay Zakah and bow before Allah.

Sura Ma'dah, Verse 55

He also declared that whoever takes Allah and His prophet and believers as friends must be triumphant. Allah says,

وَمَنْ يَّتَوَلَّ اللهَ وَرَسُوْلَهٗ وَالَّذِيْنَ اٰمَنُوْا فَاِنَّ حِزْبَ اللهِ هُمُ الْغٰلِبُوْنَ.

Whoever maintains friendship with Allah and His Messenger and those who believe (must know that) it is the (members of the) Party of Allah that are the triumphant. Sura Ma'idah, Verse 56

After receiving this assurance and guarantee from Allah, a Muslim does not need any friendship with the Jews and Christians.

The background of these two verses was that some hypocrites always maintained a good relationship with the Jews and Christians and also joined them in various conspiracies against Muslims. When questioned about their actions, they would justify it by saying that if they didn't maintain relations with them, they would be abandoned in times of crisis. They thought that if the Muslims were ever defeated by the Jews and Christians, they could then live with them. [ See Surah Ma'ida (5): 52, Tafsir Tawdihul Qur'an 1/378; Tafsir Ibn Qathir 3/132]

What an amazing similarity between the description of the Quran and the current state of the world is!