First, lets start with what may be the most famous passage in the Bible. John 3:16: "For God so loved the world that He gave his one and only Son, that whoever believes in Him shall not perish but have eternal life." And to continue on, "For God did not send his Son into the world to condemn the world, but to save the world through him. Whoever believes in him is not condemned, but whoever does not believe stands condemned already because he has not believed in the name of God's one and only Son. This is the verdict: Light has come into the world, but men loved darkness instead of light, because their deeds were evil. Everyone who does evil hates the light, and will not come into the light for fear that his deeds will be exposed."
The section in bold indicates God's love for all the world. However, my friend that I met this week believed that the "world" in John 3:16 did not include the entire world, and only referred to God's kingdom. That is why I pointed out the section in italics; it uses the same statement, "the world," but this time it specifies that there are people who love darkness in this world. That indicates that within the world the verse is talking about, there are both believers and unbelievers. Therefore, God loves both the unbeliever and the believer, aka everyone.
Now, I should make it clear that the reason my friend did not believe God loves everyone is that he believes Christ only died for some people's sins. This is directly refuted by 1 John 2:2 "He is the atoning sacrifice for our sins, and not only for ours but also for the sins of the whole world." Also, 1 Timothy 2:3-4 says "This is good, and pleases God our Savior, who wants all men to be saved and to come to a knowledge of the truth."
Two final verses dealing with the nature of God and his love are 1 John 3:16, 4:8, and 4:16.
"This is how we know what love is: Jesus Christ laid down his life for use. And we ought to lay down our lives for our brothers."
"Whoever does not love does not know God, because God is love."
"And so we know and rely on the love God has for us.
God is love. Whoever lives in love lives in God, and God in him."
God is love.
An excellent song by Gungor, entitled "God is Not a White Man", which speaks about God's love:
*One final note: one huge reason people struggle with the idea that God loves everyone is the fact that suffering, well, exists. I will try to cover that later (and maybe I did once before? I don't remember). It is a huge topic, and I certainly will not be able to explain it better than, say, C.S. Lewis does in The Problem of Pain. So if you are intersted, search around.