I believe they exsist!!!
I'm too young to remember this but my mother STILL is freaked out about it to this day.
My family lived in an old two-family home when I was around 3 or 4 years old. There were doors nailed shut and one of them had a crucifix on it (I swear I'm not making this up)...anyway...according to my mother 3 events happened that made them want to move and fast.
The first one dealt with me and the "Monkey Man" that use to visit me in my room. I don't remember any of this but my mom swears I would wake up screaming about a Monkey Man coming to get me.
The second one dealt with my brother, who was an infant at the time. Apparently, the ice cream man was coming down the street, (this I remember because it was a Mr. Softee truck!!) and I was begging for Ice Cream. My mother (for whatever reason) left my brother, buckled in his baby seat on top of the kitchen table. Her rationale was he's an infant, can't move and won't fall out so she thought he was safe...well, we came back into the house (gone for less than 5 minutes) and my brother was on the floor, STILL BUCKLED in his little 'nipnap' seat...and UNHARMED??!!??
The third and final incident involved my dad. He was carrying me downstairs and we both fell. Well he fell and naturally took me with him. I was fine, my mother asked how he slipped or what did slip on and my dad said "he was PUSHED"....he felt someone or something PUSH him down the stairs...we moved in with my grandparents the next day!!
Also, I don't know if this counts or not, but a friend of mine lives near a Hospice. More often than not when I am on the phone with her...we hear lots and lots of static and buzzing and she feels a "charge" from time to time...she's had the phone company come out, gone through phones...the phones and the lines are fine, she's finally realized that it's more than likely all the "energy passing through"....
So those are my 'close encounters.'