In my opinion they certainly do. I know several personally, and to a certain extent I am one myself. How well you do depends a lot on how willing you are to be open to 'information'. Amusingly (in a macabre way for a pilot and aiviation enthusiast) I am best at predicting air disasters, 6 so far. It is weird, since most of the time you get clues, you see scenes happening in your mind that can be either vague, or sometimes anywhere from 50-90% accurate.
To give an example, in October last year, when I was living in Los Angeles, I had a dream in which I saw a white 747 thundering down a runway somewhere in Asia (Japan was my first guess). As it rotated, its right hand maingear bogey struck something on the runway, couldn't make out what it was, but it was torn from the aircraft. It then started to cartwheel to the right, and the right wing collapsed, the tail was severed and rolled onto its side, the rest of the plane burst into flames.
There are very notable similarities between this dream, and the unfortunate demise of 9V-SPK two weeks later in Taipei, same model aircraft, struck something on the runway, right main gear and right wing sheared off, but there were also some notable differences. The location was Taiwan instead of Japan, the plane was totally white, rather than a 'tropical megatop', and the weather was calm and almost an eerie quiet, no rain, compared to the typhoon happening there at the time.
Anyway, unless I'm a total nutcase (which is probably a pretty accurate statement, lol) I do think there is some merit to 'psychic phenomena'.