Whilst any moment I've spent clearing one of the games would certainly count for this, there is one hour of my life that I will always treasure the most...
11th October, 2011.
Having been stuck behind Youmu so many times, I managed to keep most of my lives past her.
The next few minutes had my heart racing like mad. I was fighting Yuyuko; and for once, I was actually doing it.
The second I took her out on her last card, I glanced at my lives; 1 life spare. I took a deep breath and readied myself for the one card I had never faced before... Resurrection Butterfly.
With no lives and 1 bomb spare, I cleared PCB for the very first time; having started playing Touhou (which, ironically enough, was PCB) in 2009.
I think everyone on IRC that day was subject to my full on capslock approach on how I described that moment.
I'm glad you didn't ask for worst moment; because I cry just remembering it. :V