For me, mostly, it was Scar. That was probably the reason I became so attracted to TLK instead of some other Disney movie, and it was most certainly the reason I got into fanfic and got an FFn account... which, in turn, brought me here. So yeah, I have Scar to thank for everything. xP It's kind of hard for me to explain, as it probably sounds really weird... but from his very opening lines, I feel a very strong emotional attachment to him. I'm not entirely sure why - I guess because we share a lot of the same foibles and inner conflicts, and just the way he only barely manages to bridle his feelings all the time even though he's really not okay resonates with me. I'd like to think that what happens before the movie is also similar to my own story. Overall, he just... I dunno... on the one hand, he shows what can happen to seemingly normal, well-adjusted people over time, and he inspires me not to go down the same path as him, but on the other I simply find myself admiring his intelligence and his ambition.
That pretty much sums him up in a nutshell for me.
That said, I grew up with Disney movies and I did see TLK as a kid. The animation is second to none and it's just really well put together. As a creative person myself, I have a lot of respect for that kind of artistry, and I still enjoy watching this and other Disney movies today - to be honest, I usually prefer animation over live-action film in general and I find it sad how many animated 'family' movies today pander to the kiddies instead of having any real effort put into them. Luckily TLK has a good, solid plot, characters, humor, music, art, etc... making it a key example of what an animated film is really supposed to look and feel like.