The very first night I spent the night in my current apartment, my new roommate confided in me that there was a ghost. The ghost of a man who died in the kitchen. My bedroom is off of the kitchen.
I haven't yet seen the Man with the Hat (as my roommates name him) but I have experienced some things:
My roommates and I had some cocktails one night. We stayed up a little later than we should, I suppose? I got in bed and tried to sleep. I woke up to the covers being gently jerked off the foot of the bed. I sat up part-way and said, "stop it, I'm trying to sleep!" and it stopped. It wasn't until the morning that I realized that my roommates were in bed and not playing a prank on me. A few times I've woken with the sheets at the foot of the bed; if I push them myself, they tend to fall to one side or the other.
When one roommate went to visit his mother for the weekend, I perceived a man-sized shadow in his room as I walked by. I stopped and, without looking, simply said, "He'll be back in 2 days" and kept walking. There was no further activity after that.
Sitting in the den, alone, I perceived someone looking at me. I glanced up and saw a shadow dart away. I cannot rule out someone moving around but I didn't hear anything.. and it's impossible to move around the apartment without making some noise.
The closet door in the hallway began rattling one night. I put my hand on the door to make sure I wasn't imagining it when there was a muffled breath, as if something breathing through the keyhole. It stopped right after that.
So, nothing cosmic, nothing that couldn't be explained away, no messages from beyond the grave... yet. I'm keeping my senses open for this one.