No, I don't believe in it. Funny how many people here say that, but then also say "but I do read them."
Some people have the ability to read things quite accurately about a person, but it's psychological, not psychic. Derren Brown regularly demonstrates this on his TV shows. I'm no great fan of his, but I do appreciate how he makes no bones about being an entertainer and is upfront about how he has no "powers" as such but has the skill of being able to deduce all sorts of things about a person's life just from their appearance, general behaviour, responses, etc.
Predicting to the month the occasion of an illness is pretty good, and I understand how impressive-sounding that is. But I suspect they got 'lucky' with that rather than having a psychic ability, or getting it from astrological readings.