Serious answer(s):
UFOs and Ghosts.
I used to believe in the whole UFO/Aliens nonsense. I believed they had visited, I believed in Roswell, I believed in Area 51 and that the government was covering the information up, all of that. Then I turned 20 and I snapped out of it.
Now, bear in mind, I still believe in aliens. Hell I'll even accept that some alien civilization out there maybe has developed some-form-of travel that equates to FTL movement. The universe is too big and complex for that to not have happened. I'm just not entirely conviced that these civilaztions have visited Earth, have crashed on Earth (why are aliens so bad at driving their space-ships anyway) or are even abducting people just to tickle their colon.
Now, I admit I've seen "some" "UFO footage" the raises an eyebrow as being "odd" and "may be" an alien craft but I won't be convinced that it is until I see some hard-proof and not just some shaky camera of some odd lights in the sky.
Ghosts:
This is one I stopped believing in fairly "recently" that being maybe 5 years ago or so. I'd think by now there'd be harder evidence than the, like UFOs, the vauge stuff we have now. With as many people looking for it as with as cheap as various detecting and video equipment is I'd think we'd have some harder evidence.
Both still, though, make for fun movies and TV.