I don't like the term "Psychic", as it seems to lead to misunderstanding. I have had several experiences that I could only describe as "psychic". Such as sudden feelings of danger, and avoiding things mere seconds before it happens.
For example, everyday my roommate would drive us home. He would blow through the same stop sign every day, because not very many people drove through our area. One day, on the way home. I just felt he shouldn't drive through the stop sign this one time. He stopped for me, and someone else from the crossing road blew through the 4 way stop, and if he had run it like always. We would have been T-boned for sure.
I have frequently had these things, but most of the time things are not happening to "me" all the time. I just sense a certain thing will happen, and they do. Its completely random, and I only have a few seconds to react in time.
Another thing I have experienced, like Cuttlefish's post talks about. The subconscious pattern matching. I seem to be adept at this specific thing, without my foreknowledge. What I mean is that I sometimes become aware of these patterns, but only when something goes amiss. For example, I frequent forums a lot. And sometimes, forums lead to off forum chatrooms. Where people might not always use the same username. Or people might frequently change usernames. I am easily able to discern people, based entirely on my subconscious gut feeling of their typing pattern. I cannot tell you what they are, but I can pick up on those patterns. I have accurately picked out people, whom I knew. After they changed their name. A good example of this in effect, is Town of Salem. But, it does require me having communicating a lot with you to work.
Lastly, I don't know how to describe it. But I am a lucid dreamer, and have explored the subconscious quite well over more than 15 years. I would say I am a bit of an expert on dream analysis, and understanding how things affect dreams, and the waking mind. I have employed the use of lucid dreaming to confront my own mental issues. BUT, there are some things that stand out. What people would call "astral projection" or "out of body experiences", I have experienced as well. I once converted to Satanism, and experienced the wonders of isolation psychosis. Within my madness, you could say I gained a bit more insight than most people would into the construction of personality. I became far too self aware, in a sense. In my recovery, I have experienced many types of sleep disorders, and the most common among them being sleep paralysis and hypnagogic hallucinations. There were a few "Dreams" that I had, that violated all of my knowledge about dreams. They only happened a handful of times, and never again. I will list each night.
For example, I once had 3 nights of what could be attributed to many strange phenomenon. There was one bizarre incident of me waking up in bed. I have experienced sleep paralysis many times, but there was one time I woke up. I could move just fine, and I saw something standing next to my bed. A figure I couldn't see, because it was pitch black. But I could see its golden aura. It was humanoid, with 6 distinct glowing dots in its head. You could say they were eyes. I promptly freaked the fuck out, but when I turned on the light. Nothing was there.
The 2nd night, was much more terrifying, and much more real. I knew, this wasn't just a hallucination. I woke up again, to the sound of "Crackling". I have heard this sound before, it sounded like fire. I opened my eyes, and to my surprised. There was a light on in my room. But something wasn't right. The light was coming from directly behind me, and there was no lamp or anything behind me. It gave off a blueish white glow, and it was moving. I slowly turned around, and saw a ball of what looked like lightning. Hovering 3 feet above the ground, just out of arms reach. I was petrified, because I never seen anything like it. I had to tell myself it was some sort of hallucination, because I didn't believe it. I threw my covers over my head, and then it eventually vanished.
The 3rd night I awoke from a dream, and for some reason. I could see in my pitch black room. (I slept in the basement then with no windows, not even an alarm clock). I could see as if I had red night vision goggles. Everything was black and red. I sat up, and I could see my hands in front of me. I suddenly started moving without control. If you have ever been aware you were sleepwalking, it is similar to that. I somehow manifested a screen in front of myself, and I saw a page of letters I didn't recognize. I still, don't know where it came from. But I can tell you if I saw it again. I did something to the page, and black energy transferred back and forth between my hands. Then page disappeared, and I "Woke up" to the pitch black room.
Those 3 nights made me research alien abductions, ball lightning, and demonic possession more.