I have a buddy that's taking the Chester Bennington thing pretty hard, which is what inspired this thread. Personally, I felt nothing about him personally, but there have been famous people who I connected with or understood on a completely different level that when they died, I legitimately felt a sense of loss. You'll often hear people who are now in their late 30s say they felt that way about Kurt Cobain, because they felt as though he was a voice for them when they felt voiceless.
To give a personal example, I was incredibly sad when George Carlin passed away. My admiration for him went beyond thinking he was a funny comic. He influenced my way of thinking on a real level. I based a lot of my life philosophy on what I learned from him. So when he passed away, it kinda felt like a father figure dying.