Yes, anyone can have a psychic ability, and it's not just predicting things. Some people can see,hear, or communicate with ghosts, some are empathetic(and there are many kinds of empathy), some just see visions, some people can psychicly sense something about a person, some people know something is going to happen before it does but don't exactly see a vision, and some people can see energy. There are others I haven't mentioned like seeing auras or remote vision but if you do have an ability, it might not be exactly like the ones listed online(if you go to a good site), it might be a variation. Every person is different, and so is every person's ability.
For example, I can sometimes touch an object and sense the emotion from whoever has touched it, and if I'm thinking about buying something and I don't like the energy, I don't buy it. It's still psychic empathy, and I'm pretty sure the name is listed somewhere, but it isn't exactly what people think of when you say "I'm an empath"