I lived in a flat that was haunted once!
It started about a week after I moved in, the strange things happening.
Little things like putting something down, knowing 100% where I had put the item and then it disappears for days only to turn up in the fridge or somewhere equally ludicrous! As a 19yo i just put it down to being forgetful sometimes for a while...then I went to work in the club I worked weekends in and locked the bolt on the door - I know I did as my sister was with me and forgot her coat and we had to go back in so I double checked the locks when we came back out - when I got home the lock was undone and there was a large muddy footprint on the kitchen floor (but nowhere else) 
the kitchen was about 10 steps along a hallway so unless an intruder took his boots off just to leave one footprint...
I changed the locks the next day and got another bolt for the inside...so anyway, the following weekend when I got home the key wouldn't go into the lock properly so I couldn't get back in. I rang my dad who came and kicked the door in as he couldn't get it open only to find the spare key in the back of the lock, the lock on and no one in the flat!
I wasn't all that scared but decided to give the spare keys to my mum so the same thing didn't happen again...
About 3 weeks later, I was in bed on Sunday morning after working til 4am and the landline rang. I ignored it as the phone was in the living room and I was in bed and the phone stopped after about 3 rings so I didn't worry about it. About 5 minutes later my sister rang me on my mobile (big old Nokia phone 
) and asked why I had answered the phone how I did. I hadn't answered the phone and told her this. She then told me that the phone rang three times, was picked up and someone whispered "Yes, Hello?" I laughed and said that was impossible, she must have had the wrong number. I decided to go and check as my sister said she had tried to call back and the line was engaged. When I went not the living room, the phone was moved to the top of the telly in the corner so the wire was stretched taut from the socket and the handset was out of the phone cradle!!! WEIRD!
I moved out after 6 months and the housing officer asked why so I told her. She then laughed and said she had thought the last tennants had been lying!
Apparently the people who lived in the flat before me had complained that there had been intruders in the flat a number of times and blamed other tennants in the building...they also bought a new flashy (then) TV - one of those big heavy ones with a box on the back- and it would switch itself off by the plug on a regular basis and then one day they went out for the day and when they got home they fond the TV wedged tight in the bath...they moved out the next day...