"Hate the sin, love the sinner" is a common Christian cliche that receives mixed criticism. Some say it is 100% biblical. Others say it is illogical, even to the point of claiming that, since God condemns the sinner to Hell, He obviously hates sin and sinner alike.
Is this reasoning valid? Consider Romans 5:8: God shows His love for us in this: while we were still sinners, Christ died for us. Clearly, God hates sin. There is no possible way, unless you happen to come across a man named Sin, to say that God loves sin. However, the cross is proof that God is perfectly capable of loving sinners in spite of their sin. If God hated sinners, there would be no grace. If we were free from Hell for even a time, as Satan is, it would not be for purposes of grace. We wouldn't have the capability of repenting, we wouldn't have the offer of salvation, we would be doomed without hope.
Yet we are not. Many people alive today are not only sinners, but are not saved. Yet. But did Christ not die that they might be? If an atheist converts today, will he still be doomed tomorrow? If He dies in a state of impenitence, then he will go to Hell, but this is not because God hated him, but because he hated God, so much so that he refused to become separated from his sin.
Ultimately, God commands us to love even our enemies, so that we may be like Him (Matthew 5:43-48). If we are commanded to love our enemies in order to be like God, the only logical conclusion is that God loves His enemies too. Therefore, "hate the sin, love the sinner" is completely biblical.