In the musical it's always the Circle of Life for me too, there's just something about it that's so powerful and wonderful. Makes me tear up every time.
That definitely goes for me with the movie as well. My theory is that because I've have more emotional life experiences that can relate to more of the scenarios in some way, they tend to affect me more, at a guess anyway. When I was younger I would sometimes only cry at Mufasa's death. These days however, I tear up when Mufasa is telling Simba about the great Kings of the past, when Mufasa dies, sometimes at Mufasa's ghost, and also when Simba is ascending Pride Rock at the end. I've really got to get it under control
I'm going to have to watch the movie again soon to test that out, it's been a while so I'm probably due for another TLK cry