There have though been many experiments made to do with telepathy. One is done by having people who believe themselves to have telepathic abilities to phone one another, and to have them guess who was phoning before they answered.
The Nolan Sisters were very famous in the UK in the 70s, and have been a household name ever since then. Being sisters and very close in their relationship together, they had always said they were telepathic, and knew what the others were thinking about. For this experiment one of the five sisters went off to another location, and the other four had to phone her separately, and she would have to guess who had called. All being done on camera, and the results being taken down carefully and scientifically.
The results which came out were that Coleen, the sister doing the guessing was right 50% of the time, which although not 100% correct was still better than that which would have been expected by pure random chance.
Although it is of course possible to beat the odds by pure chance, this experiment did nevertheless go some way to suggest that there may well be something more to telepathy than first meets the eye.