I have four experiences that weren't too scary, but could have gone badly.
1: I running along a bridle path with some ferns/shrubs along it's bank, and suddenly heard some barking/growling behind all those plants. I looked up and came face to face with this unleashed black guard dog of some type, staring right at me and looking like it was going to charge at me. I just stared for a few seconds and then kept running, hoping it would ignore me. I now realize this was an incredibly dumb idea, as dogs instinctively chase what runs, and this one looked really pissed off to start with. Luckily, he did just ignore me, and nothing came of it.
2: I was in the last 200m or so of my run in heavy rain. I suddenly heard a REALLY loud thunderclap, and saw a lightning bolt strike horribly closely to me. I SPRINTED home, but this was actually less scary than number 1, because the lightning happened too fast to really engender fright. I didn't feel scared running back, but then I didn't feel anything - it was like my body just activated and said "let's get out of here, you can think about it later".
3: Running along an isolated bike path in a really rough area at 3pm on a Saturday. I would not have done this normally, but this was when I was new to the area and didn't realize how unsafe it could be. I hear a swarm of motorbikes behind me, and turn to see a gang of 4 on an obviously stolen motorbike riding towards me. I stopped and turned to face them, and played as dumb as possible - played it like I had no idea what was going on and was just nicely letting them pass. They might well have just gone past, but what actually happened was they all freaked out, turned 180 degrees, and high-tailed it out of there. I was mystified for a minute - did I just scare off a gang of people by stopping and turning like Schwarzenegger?Do I have a new career as a superhero? No, actually - there happened to be a cop right behind me, who was acting on a call of a gang of bike thieves joyriding up and down the trails.
4: Running during lockdown, and didn't want to run over a 200m bridge that was only about a metre wide and had people walking in the opposite direction all along it. I stick to the road, running in the cycle path, then jump up onto a slightly uneven concrete part of the bridge that is further from the cars than the cycle path out of courtesy. I run slowly along this, then stumble for a second, and just keep going. It wasn't until about a minute later that I think that if my toe had caught the jutting stone at a slightly different angle, I would have likely had my head crushed like a watermelon by a truck.
5: Age 12, new to running, and decide to run 5 miles for one of the first times ever. Realized I had to sh!t 2 miles in, but back then I had this mentality that if I stopped for ANYTHING unplanned, be it a shoelace, a car, or... this issue, then the run didn't count and I'd be furious with myself for the rest of the day. So I kept on. My God, the last half mile was a race against nature. I couldn't speed up as opening up my stride would release the brown tides, but I couldn't stay the same speed as I might not make it to my porcelain throne. I somehow made it home in time, and that was the end of that mentality. This was the longest-lasting descent of terror I've had on any run.
Another weird/creepy thing related to running, but that din't happen on my runs, include being turned away from my usual route by the police because a man who used to live a few doors away from me in a different town had been found murdered on the trail 300m away, right next to where I would run almost every day. I believe the crime is still unsolved, but it was strongly suspected to involve gangsters and a property deal - the guy was a property broker in his 40s/50s, and had been killed "professionally".