Psi research, while condemned or dismissed as pseudoscience by many mainstream intitutions and researchers, is alive and kicking on the internet via a number of online experiments. They allow for an assesment of one's own "psychic" capabilities and also serve as data collection tools for ongoing psi research. These experiments are, on the whole, rather well designed and amusing to participate in. For example, in the Fourmilab retropsychokinesis project, the participant is asked to try to influence a stream of random data generated by measurements of radioactive decay, a source of true quantum randomness. Then the results of the experiment are cataloged and along with those of thousands of other participants, and the resulting data is searched for statistical anomolies. To participate in any of these experiments, visit one of the following sites:
The Retropsychokinesis Project
IONS Intuitive Diagnosis Experiment
In a similar vein, also check out Princeton University's Global Consciousness Project.