Safe Cracker game: Choose a difficulty level by entering the number of digits you want in the combination.
ESP Tester: based on Russell Targ's device, as described it in his book "The Reality of ESP" for Windows, "guess the next pseudo-random colour or pass." The "pass" option cuts down on the force-choice problem, so the player can skip runs that they don't "feel right" for. (This is still in development,... a few minutes here, a few minutes there...)
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(Note: very much non-exhaustive list)
Target Pool, on Lori Williams' site. Scroll down to the bottom to find the list.
ARV Tools, on Martin Zvarík's site. He has a nice set of targets, placeholders, and stuff here.
Telepathy, search results in CIA Reading Room
Stargate, search results in CIA Reading Room
Section IV - ESP and Psychokinesis, sanitized excerpts from a report.