I recently found out that a PET scan stands for a positron emission tomography. Are there any other practical uses of antimatter in the present?
I don't know if the other antiparticles have been exploited, but positrons are used in metallurgical studies. Positron annihilation spectroscopy is one particular application.
I don't know if this counts as "practical", but antiprotons are used in the Tevatron to increase the center-of-mass energy of collisions with protons.
In the LHC, however, the rest-mass is so much smaller than the Lorentz-boosted mass in the center-of-mass frame, that it basically isn't worth the hassle of using antiprotons.
This may just be a quirk of historical naming, but anti-neutrinos are typically much more common than neutrinos, since they are formed via beta-decay, which is happening all around us all the time.