One interesting 'practical application' of cosmic-rays is in how they may affect life on Earth.
The obvious effect is that cosmic-rays are responsible for a good chunk of the background radiation that we experience on earth (the Earth itself is responsible for most of the rest, in the form of natural radon gas, etc.).
Of course, a dramatic short-term increase in the background radiation is dangerous. An overly nearby supernovae or other high-energy astrophysical events would be deadly (but very, very rare); it has been speculated that they may be responsible for occasional mass extinctions.
The long-term effect of lower doses of radiation, as from cosmic-rays is less clear. Cells contain repair mechanisms which can repair chromosome damage if it occurs slowly enough, and experimental studies of low levels of radiation have not found an increase in mutations. But, increased radiation level could cause increased mutation rates, and it has even been speculated that moderately nearby supernovae could have aided human evolution. Of course, in the shorter term, most mutations are not beneficial. It has been argued that the increase in ground-level radiation during reversals of the Earth's magnetic field could lead to increased mutation, and possibly, even to extinctions.
These supernovae leave geochemical 'footprints' on earth. These footprints can be seen in the form of thin layers of otherwise rare isotopes and an increase in carbon-14 abundance. The changing production rate greatly complicates the use of carbon-14 for dating, and elaborate calibration curves have been needed to relate the measured carbon-14 abundance in artifacts with the actual age.
Of course, this is mostly speculation. Interesting and important speculation, but still speculation.