I have yet to have a primer not go off without a specific reason. Some didn't go off due to lite strikes or improper seating, usually by someone else, deformed cases or something like that. My own reloads I have never had problems with, especially those that are specifically for self or home defense.
I have no problem handling primers but I make sure my hands are clean & dry when it comes time to prime cases. No sweaty fingers, oily fingers or greasy fingers allowed! Primers I find on the floor (unless I just dropped them) get used for practice ammo.
I have used Winchester, CCI, and Federal primers for the most part and a few times got Remington if the others weren't handy. I've never had a problem with any brand and I've reloaded well over 1 million rounds (I had a commercial reloading operation using 2 Dillon 1000... which should hint at how long ago it was!) and never had problems with any of the major brand names. I know others who say they have but I've never personally experienced it.
Cheers,
crkckr