I have a few of these odd/woo stories. My favourite is one my Nan told us. My Nan was not a remotely 'woo' person, she was very rational and level-headed.
One night she awoke in the middle of the night to find a figure standing at the end of the bed. She started (as you would) before realising it was her next-door neighbour, with whom she was friendly. She said "what are you doing here?" but when the neighbour didn't reply, Nan assumed she was just half asleep and lay back down and fell asleep again.
The next day she discovered that her neighbour had died last night, at about the same time that she'd woken up.
I have always been prone to seeing and hearing odd things. I remember on occasion, when I was a teenager, hearing my Dad come through the front door. I heard his keys and the doors slamming shut. I waited for him to come in to the living room, but he didn't, and I hadn't heard him go up the stairs or go back outside again. After about five minutes, I went out in to the hall, wondering what he was doing. Except that there was nobody there and his car wasn't outside; he hadn't come home yet and nobody had been through the front door.
Also vividly remember the time I was at home with my mum, dad was at work, and the phone rang. I instantly KNEW that it was my dad and he'd been in an accident. There was no reason to think this - the phone regularly rang in the daytime and it was always sales people etc - but I just knew. I was quite correct, dad had been in a horrible crash (he was a lorry driver. thankfully, he came through it just fine.) I still cannot explain why or how I had this feeling.
I quite often see shadowy shapes moving around the house and see a cat out of the corner of my eye. I have always had cats around me and naturally have lost a couple over the eyes so I don't know if it is them hanging around or just my eyes. I've never felt threatened or bothered by it.
Many years ago my Mum asked me to help her find some money she'd misplaced. I can't remember the amount but it was in note form. She'd last seen it in the kitchen so we basically dismantled the room - moved EVERYTHING, looked in and under everything, checked every cupboard, etc etc. Eventually we decided to give up as the money was nowhere to be found and put everything away again. We make a cuppa, then we turn round and see the money just lying there in plain view on the kitchen counter. It is literally impossible that we wouldn't have seen it before and there was nobody else in the house, so no one was playing a joke on us. Mum and I just stood there looking at each other!
This is the last one I can think of at the minute... my Nan died a few years back. I'd gone to visit my parents, and they gently broke it to me that she'd passed away peacefully the night before. I was extremely upset, and later on, as I was trying to calm myself, the smell of Nan's perfume filled the room. She wore a very strong perfume and it was always very noticeable around her. I was really puzzled by this as there was nothing of hers in the room and nobody in the house was wearing perfume but I decided I was imagining things because I was upset. I didn't say anything because I didn't want to upset my parents.
Years later, my dad brought up in conversation that he'd smelt her perfume that day. He hadn't said anything before because like me, he didn't want to upset anyone. There is no way we influenced each other because neither of us mentioned it at the time.
I now feel very comforted by it as I believe Nan came because I was crying. I still associate the smell of that perfume with her.