I have unbelieving friends, but they are not as close as the believing ones - mainly because my heart is on my sleeve and it does create a distance.
Kvan, example from this morning. when i parked my car at my office building (the church rents an office in a business centre) a man going in at the same time stopped me to talk about his marriage breakdown and ask if we could go out to lunch and asked me to pray for him.
He is a non-xn that I met and became friends with 5/6 years ago. we get together a couple of times a month. He visits our church rarely, holidays that kind of thing. I always ask what I can pray for him for when we part & I usually pray on the spot.
I find asking how to pray for people goes over very well, with 99+% of people & the nature of your friendship is open. they often become closer to you after you begin praying with them. in my opinion prayer evangelism is a much neglected tool.
All of my friends are not believers (the one's I know in person), before you get angry this is because I 1) Can only attend church occasionally because I cannot drive 2) The lack of people in my school that are Christians beyond "family" or being nominal. I still stand for the truth of God when the situation comes.