What is the Biblical basis for "hate the sin, love the sinner"? The expression "hate the sin, love the sinner" gets thrown about in both Christian and non-Christian circles, but it does not seem to be a bible verse.

What Biblical concepts support this popular cliche? And what supports it being applied to men and not just God? Some say "that's the way that Jesus lived". Are there examples of Jesus' conduct that demonstrate this one way or another?
I think "hate the sin, love the sinner" is a very Christian concept.

God hates sin, and in fact he hates sinners.

Romans 9:10-18


  10 Not only that, but Rebekah’s children were conceived at the same time by our father Isaac. 11 Yet, before the twins were born or had done anything good or bad—in order that God’s purpose in election might stand: 12 not by works but by him who calls—she was told, “The older will serve the younger.”[d] 13 Just as it is written: “Jacob I loved, but Esau I hated.”[e]
  
  14 What then shall we say? Is God unjust? Not at all! 15 For he says to Moses,
  
  “I will have mercy on whom I have mercy,
     and I will have compassion on whom I have compassion.”[f]
  
  16 It does not, therefore, depend on human desire or effort, but on God’s mercy. 17 For Scripture says to Pharaoh: “I raised you up for this very purpose, that I might display my power in you and that my name might be proclaimed in all the earth.”[g] 18 Therefore God has mercy on whom he wants to have mercy, and he hardens whom he wants to harden. 


We see here that God chose to hate Esau before he was even born. He chose to harden Pharaoh in Egypt for his own purposes.

However, we do not know who God has elected to save and so we should treat everyone with the love and respect that he has given to us. 

Matt 22:37-40 (NIV)


  37 Jesus replied: “‘Love the Lord your God with all your heart and with all your soul and with all your mind.’[c] 38 This is the first and greatest commandment. 39 And the second is like it: ‘Love your neighbor as yourself.’[d] 40 All the Law and the Prophets hang on these two commandments.”


We are to love our neighbors (a pretty expansive group, potentially all we come into contact with) as we wish to be loved. This is a huge command. We are to love everyone in our lives as much as we love ourselves (be honest its a lot). 

Loving others is our greatest command at this point 

Romans 13:8 (NIV)


  8 Let no debt remain outstanding, except the continuing debt to love one another, for whoever loves others has fulfilled the law. 


God's perfection cannot tolerate sinners. However, we are by no means perfect creatures and have little to no right to render judgement upon a creature god has created. Thus we should live as if each action we take and word we speak are towards each other and those outside of our circles are towards a brother in Christ, because we can not see who God has chosen and who he has not.