What are some bible verse proving God's unconditional love?

I can totally identify with your friend. I used to feel the same way. There are some good verses here that others have listed, my problem for a long time was all the "religous doctrine" that had been thrown at me for years, which made me feel like I was unworthy and had done so many things wrong and thats the major problem in others as well, but the fact is there is no big or little sins, we all sin everyday and we all fall short of the glory of God. I am no better than anyone and God doesn't love any one more or less, no matter what they have done or who they are. But in order to truly understand this we must come into a relationship with him, forget what others say about him, but find out for yourself study the word but ask God to help with understanding and even ask him to help you to see how much he loves you and he will because he did it for me, he brought me out of years and years of depression, so I know that he can do it for others as well and I just cant understand why so many no matter if you believe in God or not would want to take that away from someone. If someone has found true joy, peace and love in God, people will always try to come against it, "religious people" and "non believers", but no matter what you believe you should not try to take someones happiness and peace away from them.