Specifically with regard to the Harry Potter world.
If you don’t know: a boggart is a type of spirit that feeds off your fear. It is a shape shifter, so it will always take the form of the thing you fear the most. Scared of spiders? It becomes a giant one.
After long and careful thought, I think my boggart would appear as a ringing telephone. Not really scary in and of itself. But an incoming call, especially from an unknown caller, pretty much pegs my dread meter.
A room full of people, formally dressed, none of whom I know and all of whom are looking to interact with me.
Talking aloud to people. Pretty much anybody. It’s not that I can’t speak. It’s more like I’d rather not. If it’s real important I can force myself.
I’ve found I do have things to say and lots of words rattlin’ around in my head. So I fill journals. Lots of journals.
And now the SDMB. Sorry, but I must. 
Vicissitudes of aging.
I have a fear of grizzly bears and accidents while handling poisonous snakes. I love snakes in general but I get kind of jittery while handling dangerous ones. They tend to come up in my nightmares now and then.
OK, I’m showing my age but -------- I expected this thread to be about things you don’t want to share. :smack:
Wasps. They don’t even need to be giant, just a few regular-big ones buzzing about the place would freak me right the hell out. I’m getting goosebumps just thinking about it.
My boggart is tricky, I can’t think of one off hand.
My first thought also, as in “Don’t Bogart that joint man.” from my youth.
“Jittery” would be a vast understatement of what I’d feel if I had to handle a dangerous snake. I don’t mind mundane snakes, and have happily walked around with a friend’s pet ball python draped around my neck. But I’d piss myself if I had to hold a venomous snake behind it’s head, hissing at me, thrashing around. Yeesh.
I was thinking I didn’t really have a boggart until you brought this up.
Edit: How often, and why do you have to handle dangerous snakes???
Just a hobby, I always had a fascination with reptiles. I haven’t handled a dangerous snake in decades and have only done it on a few occasions very carefully.
Dogs.
Tsunami
I’d tell you, but I think she stalks me here.
The mule of course.
Unafraid to hijack my own thread: I’m 13 years older than my Missus. When we were watching Harry Potter movies with the kids and they started talking about boggarts I was the only one in the room chuckling, nobody else knew about bogart. In fact, it was only a couple months ago I introduced the missus to the term, and shortly afterward, the song.
Bugs Bunny. Duck Dodgers doesn’t scare me in the least.
IRL: Centipedes and millipedes.
Professor Snape.
I always though that scene in the book is unrealistic. Every kid immediately mentally identifies their own worst fear and are correct about it?
Wait, what? I didn’t think that the kids all knew what their fear was until it leapt out.
I don’t remember how it was presented in the movie, but in the book Lupin says something like “take a moment to consider what your boggart will be and how you might make it humorous.” Then all the kids start whispering to themselves about what they are going to do to their boggart.
Except for Harry, who figures out what his boggart will be but doesn’t come up with a plan to deal with it.
Hmm.
My brain is now jumping to the theory that the boggart might only read your mind enough to find what you believe you’re afraid of, meaning that you can actually control what the boggart shows you, by focusing on one scary thing specifically. It also explains why kids end up seeing such transient things like Snape and a bad test score while still respecting the “we’re too afraid to even say Voldemort’s name” rule a decade after his apparent death.
ETA: And to bring this back to the thread, while I said “dogs”, there are almost certainly things I would find scarier than dogs (like, say, tigers), but i don’t run into tigers on a daily basis, so they’re not on my mind.