I do believe in them, and here's my experiences...
When I was about 10, I lived in Taiwan, and my aunt found a cheap studio apartment across from a cemetery. In Taiwanese culture, we have a tradition where a temple opens the gates of a temple (
Wiki explains best), and during this month, all sorts of strange things happened, especially at my aunt's apartment: The intercom/buzzer would ring randomly throughout the day, but the camera would not show that anybody is there: Keep in mind the lens had a fairly wide angle so you can see if someone was hiding, not to mention the intercom sequence is having to punch in a 6-digit number and you'd have to press and hold the button to have it ring, and it would keep ringing even when we're looking right at the intercom monitor... Also lights would flicker, I'd come over and a bowl is broken, and the most weirdest of all: At night, I still have never saw a dog do this: She stared out the porch towards the cemetery, her eyes were wide open, and her tail would stick straight up (when it usually curls towards her back) and wag to about a 45° angle left to the side and hold, then about 2 seconds later, to the right, and make a quieter-than-usual drawn-out bark (it wasn't quite a howl, growl, and it wasn't the usual loud and short bark dogs do; hard to explain), and I'd see a purplish glow.
Fast forward to about 12 and back in the US: In my dad's house I never bothered to redecorate my room yet, and there was a painting of a ram glued to the wall (which I later found out was used to hide a hole he punched in the wall when my diagnosed-antisocial mom pissed him off)... Anyway, I wake up for something routine (bathroom or water, I forgot), and I see its eyes glowing green in the dark. I panic and try to turn on the light, which was a fluorescent fixture that used a glow-type lamp starter instead of an instant-on ballast or even electronic starter. This time, it took 5-6 seconds just to warm up, and the flickering is more slower and pronounced and took almost 4 seconds (when usually it warms up for half a second at the most and is on within 2 seconds). When the light eventually came on, the whole side of the closet wall had all these quarter-inch black dots, and they disappeared one by one. Needless to say, that ram was covered up by a poster of an E46 M3 and bought an electronic starter that weekend.