Not really sure I want to since I was dumb as nails as a kid. I mean, intellectually and academically, yeah, I was the best, but with everything else...

Ehehe... not so much.
But you asked, so here's an example (just the first of many that springs to mind). When I was about 6, I honest-to-God believed that only guys could die while sleeping. Females, for whatever reason, couldn't. I think this belief persisted until I was about 10. Sounds weird, right? Well, there's a reason for that. I was extremely, extremely gullible.
So. Imagine me. I'm like 5 or 6, a little kid, super gangly and awkward and kind of a know-it-all without trying to be, so I don't have a ton of friends, at least in my own grade. But there's this 5th grader who seems to think that I'm the most adorable thing after newborn kittens, so he doesn't mind me bugging him. He would entertain me with stories and stuff like every day on the bus ride home. And he had these girly friends who he hung around with.
So he showed them off to me one day, since I didn't really have anyone else to talk to, and they all thought I was so cute, right? Well, yeah. All the girls loved me since I was so adorably little, I guess. But of course he decides to go all macho for them and tell them (and me) a creepy story. Everything went fine until the part when the old guy/main character of the story went to sleep and died.
Of course, to a six-year-old, that's scary. I immediately started thinking that that could be me, and I could literally just die at like any moment if I fell asleep. Yeah. Frightening. So I pretty much just gave this reaction of "...
whaaaaaaat? 
" and instantly burst into tears.
Now, nobody wants to be responsible for some poor little kid crying her eyes out. Naturally, their reaction was to try to calm me down ("awwww look, she's crying, how sad"

), but as it turned out, the only way to do that was to reassure me that it only could happen to guys. My gender was notably exempt for whatever reason. That worked.
Luckily I never told anyone about this 'belief' I had, I just kind of realized what happened years later while thinking about it.

But yeah, just one example of weird crap I did and thought as a kid.
*weird story over*
On that subject, what's your best childhood memory?