I would likely kill myself out of pure excitement if I came across a wild snow leopard. Sadly, however, these animals are very rare and one would likely never see one outside of a zoo, even within their very small range of distribution.
As for animals I have seen in the wild, I've always had a fondness for black bears. They are very intelligent animals, and also relatively harmless as they are non-aggressive and typically only attack if they feel like their cubs are threatened. Seriously misunderstood animals, and it breaks my heart whenever they get killed for wandering into town because of human error. All they want is food, and we humans are not food to them, we just leave it out as an open invitation and cost them their lives. It's sad.
Plus 1 for the hundreds of wild rabbits I see around here.