Time/dimensional shifts
When I was a kid, the only time-shift story that seemed to be discussed (endlessly) in the books about the supernatural that I read was the Moberly-Jourdain one at the Petit Trianon. I could conveniently discount that though as probably just being the imaginings or misconceptions of the two witnesses.
Nowadays, there are a multitude of accounts of supposed timeslips (albeit of varying degrees of reliability). The internet has provided us with a means to diseminate and gather such accounts that would have been unthinkable even thirty years ago. On the whole I've been forced to consider that such events may
actually occur. They've become one of the Fortean areas of interest that I'm increasingly convinced will be shown one day to be genuine.
Alien Big Cats
I've always believed that these are real, flesh and blood creatures living and breeding in the UK. My parents and uncle and aunt saw one in the West of Scotland one summer when we were on holiday there. However, beyond that; there are too many people - many of them well versed in the wild (and domestic) creatures of Britatin, who believe that they exist. It's not a subject on these boards that I visit very often; as far as I'm concerned it's 'case closed'.
Ghosts
I believed in ghosts utterly when I was young. Then came to disbelieve. Now, I'm back in the believers camp. Most I think are images - just glimpses, of people or events from the past (through what mechanism I don't know). A few (very few), though, seem to be actually sentient. Which is worrying as it suggests that there
is something after death (which is a concept that I'm not really comfortable with).
My uncle saw a ghost; only to be laughed at by the whole family, later his account was corroberated by a previous resident of the same house who had seen the same thing years previously. I believe they exist.
Life after death
Gah!

I just don't know. If I believe in sentient 'aware' ghosts (or apparitions/spirits/shades/phantoms/call them what you will), then that means that there actually
is something after death. Which, presumably, means that I should be doing something to improve myself spiritually or to help others (although, if I'm doing these things to ultimately bank karma, that's not very altruistic of me is it!). Which, being the self-centred, selfish bastard that I am is not going to happen. If there is such a thing as reincarnation; I'm screwed!