In which reference frame? For every particle and for every speed below the speed of light, you can find a reference frame were it travels at this speed. With the exception of massless particles, they always travel at the speed of light.
Relative to Earth, the fastest particles accelerated by humans were electrons in LEP at CERN, at 0.99999999999 times the speed of light (the 9s are counted). The fastest particle observed came via cosmic rays at 0.999999999999999999999995 times the speed of light.
If you are interested in thermal motion: This is just a matter of finding the lightest particles. Hydrogen atoms at room temperature have a speed of the order of 1 kilometer per second, or 0.000003 times the speed of light. Free thermal electrons would be faster, but having them at room temperature requires very odd conditions. Free thermal neutrons would be even faster, but there is no realistic way to produce that now.