As Christians, we have to constantly face temptations and the attacks of the world around us. Everything we see, read, do, hear, put in our bodies, etc., affects us somehow. That's why, to maintain a close relationship with God, we have to put aside our old ways of doing things—the things we watch on TV, old bad habits (excessive drinking, smoking, etc.), the activities we participate in, and the people we spend our time with. People are divided into only two categories, those who belong to the world and its ruler, Satan, and those who belong to God (Acts 26:18). These two groups of people are described in terms of opposites all through the Bible; e.g., those in darkness/those in the light; those with eternal life/those with eternal death; those who have peace with God/those who are at war with Him; those who believe the truth/those who believe the lies; those on the narrow path to salvation/those on the broad road to destruction, and many more. Clearly, the message of Scripture is that believers are completely different from nonbelievers, and it is from this perspective that we must discern what kind of friendships we can really have with unbelievers.
The book of Proverbs has a few wise verses on believers befriending non-believers: "The righteous should choose his friends carefully, for the way of the wicked leads them astray" (Proverbs 12:26). We should stay away from foolish people (Proverbs 13:20, 14:7), from people who lose their temper easily (Proverbs 22:24), and from the rebellious (Proverbs 24:21). All these things represent those who have not been saved. "Do not be yoked together with unbelievers. For what do righteousness and wickedness have in common? Or what fellowship can light have with darkness?" (2 Corinthians 6:14). First Corinthians 15:33 tells us that bad company corrupts good character. Unbelievers are slaves to sin (John 8:34), and Christians are slaves to God (1 Corinthians 7:22). If we become deeply involved (either by friendship or a romantic relationship) with non-Christians, we are setting ourselves up for turmoil. It can (and does often) cause the Christian to stumble in his walk, fall back into a sinful life, and also turn others away from God (by misrepresenting God and Christianity). Another detrimental effect of closeness with unbelievers is our tendency to water down the truths of Scripture so as to not offend them. There are difficult truths in the Word of God, truths such as judgment and hell. When we minimize or ignore these doctrines or try to "soft pedal" them, in essence we are calling God a liar for the sake of those already in the grasp of Satan. This is not evangelism.
Although these close relationships are not recommended, it does not mean we turn our noses up and ignore unbelievers, either. Second Timothy 2:24-26 tells us that as servants of the Lord, we are to be kind to and not quarrel with anyone. We should gently teach those who oppose the truth, and be patient with difficult people. Matthew 5:16 tells us, "Let your good deeds shine out for all to see, so that everyone will praise your heavenly father." We should serve unbelievers so that they may see God through us and turn to Him in praise. James 5:16 says that there is great power in the prayer of a righteous person, so bring your concerns for unbelievers before God, and He will listen.
Many people have been saved because of the prayers and service of Christians, so don't turn your back on unbelievers, but having any kind of intimate relationship with an unbeliever can quickly and easily turn into something that is a hindrance to your walk with Christ. We are called to evangelize the lost, not be intimate with them. There is nothing wrong with building quality friendships with unbelievers, but the primary focus of such a relationship should be to win them to Christ by sharing the Gospel with them and demonstrating God's saving power in our own lives.