My special moment was similar to that what Furvan experienced:
I was one of the last suiters in the zoo. Taking a little break and waiting for the last bus to arrive, I sat on a bench in the public area (still in my suit). A family (granddad, grandma and two children) approched me. The dad was really excitied, going on about that they finally found "one of the special creatures", and what a fine example of a wolf they had found here, how soft my fur was, how nice my claws were etcetc. Not only that he was totally flattering me (and I was happy that they could not see me blushing under the suit), but he was also more taken away by the magic than the kids, who just stood there gaping with their mouths open. I think I have never seen an non furry adult getting so enthusiastic about a fur suiter in my life.
Finally - after tons of hugs and fotos - they left, and it was time for me to go as well.
I changed, got my bearings, and went for the exit of the zoo. On my way, I passed the four of them sitting in the cafeteria. As I was already carrying a suspiciously big box (with my fursuit inside) and the granddad watching me thoughtfully, I just gave them a little wave and a smile. His eyes went big, and he asked his family:"Is that the wolf? I think it is the wolf!" I had to laugh hard, but just shrugged, gave them a little wink and walked on, followed by the granddads excited comments: "Yes, I am sure of it, it is our wolf. It is really him..."
Later that week, at the parade, I actually met them again - twice! They doubled back after I passed them the first time so they could see and greet more of "their" wolf, how they kept calling me since the zoo.
That whole experience really warmed my heart, and puts a smirk on my face every time I think about it. I never thought that bystanders could get so attached to suiters (whom they never met before) as to follow them/look out for them and get so happy when they find them again. It shows me once more how much joy and delight a suiter can deliver to all the (non furry) people out there, and how much appreciated the fandom can be even by non furries.