Since I've yet to make any memories with my own family, I'll bring up two from my childhood (both involving the rain at Disney). The first is actually my profile pic; it was at MK somewhere in Liberty Square. It had started raining, and me, my sister, our mom, and our grandma were looking for cover when we saw cast members gesturing that people could go wait in this building/lobby area. Inside it was crowded, but we were surprised to see it wasn't just people-- Chip, Dale, Pluto, and Mickey were there, too! We got pictures of us (soaking wet!) with all of them.
The second memory was short, but my sister and I have never forgotten it. We were in the world showcase at Epcot, and of course, it was raining again. We had on Mickey ponchos but my sister was still getting wet sitting in the stroller. We were walking towards the park entrance when this lady dressed in a business suit (I remember thinking she must have been very important to be wearing that in the park) was walking by and approached us, giving her black mickey umbrella to my sister. We thought it was the coolest thing ever! The only bad thing afterwards was when we got home from our trip our mom took it to 'save it' and we were never able to find it again.