All electricl plugs have power and neutral. the metel box that they are housed in of older houses should be grounded (newer house have platic boxes, but with 3 wire ran, it's same difference). if you buy the adapter and screw the tab on the middle of the box, you have an effective ground. expect in some cases.
if the 1960's a lot of electrician's cut corners for some reason or another and the boxes aren't grounded or they only gounded the kitchen and bathroom boxes, because those obviously need protection. those houses are more susceptible to fires too as they don't have that extra level of protection.
Stray Electric will short to ground faster causing your breaker to pop plus your electric is more stable. If your outlet isn't grounded a fire will ensue before the breaker pops. static will also short to ground too and leave you.
you should buy a circuit tester (1-2 dollars) if your home might fall in the above category.