I didn't cry when I was a kid. I felt bad for Simba, but I guess death didn't really hit me that much. When you're young, you tend to think yourself and those around you immortal, especially if you are raised (as I was) fairly sheltered from death.
Now that I'm older ... I skip that part over because otherwise I cry every time. :p
Another sad scene (for me) is Mufasa's ghost coming back. I've never cried at it, I just get rather depressed. I wish Simba had shown a teeny bit more emotion after all that, but oh well. :3 It's still a really powerful scene.