I can't remember any exact battle scenarios that were close calls(I know there were some), but my closest call that I still remember was my first playthrough of soulsilver and I got to Articuno, but forgot to save before I battled it. I weakened it and paralyzed it but still couldn't catch it. I ran out of Ultra balls and all I had left was a Master Ball and one Great Ball. I just knew I was going to have to waste my masterball, but to my surprise I through the Great Ball and CAUGHT IT! Very close call!