I've not seen any convincing claim of psychic powers yet. Every time I look for incontrovertible demonstrations of such powers, I am always left utterly disappointed. It appears that people who make such claims simply don't scrutinize their beliefs and intuitions voraciously enough. I'd love for there to be some magical element in the world, I'm not against supernaturalism, but the fallibility of human judgement is too great to trust any anecdotal evidence or personal intuitions.
"What holds attention determines action." - William James