There exists differing views on Sai Baba, and whether his abilities are real or just stage magician tricks. See for example this article in English from 'Sökaren' ('The Seeker'), a Swedish magazine for spiritual/new age issues: http://www.sokaren.se/INDEX135.HTML
There are a lot of stories going around about people with extraordinary abilities, and I certainly would not say it's totally impossible (I've experienced a number of interesting things myself that I could not immediately explain, like mind-reading, premonitions and "visions" ). Still, people often have so much to gain from painting themselves as "OTs" - fame, attention, admiration, power, money, sex - that I think one should be very wary about uncritically accepting such claims.
Another thing to remember is how tempting it is for many of us to believe such claims. Fantasy stories are great fun, wouldn't it be interesting to live in a colourful world with magic everywhere? I personally would really love to believe that all tales of extraordinary abilities are true. Which is precisely why I have to be extremely skeptic about them, or I'll just fool myself with wishful thinking. That goes for personal, subjective experiences as well - there is a difference between what goes on in my mind (no matter how "real" it feels) and logical, outside-world explanations of what is going on.
"Reality is what doesn't go away when you stop believing in it." - Philip K. Dick