From page 26 of the current owner's manual;
This model of the PlayStation®3 system is designed to play
PlayStation®3 format software and has limited backward compatibility.
This system is not compatible with and will not play PlayStation®2
format software. Some PlayStation® format software may play on this
system. For more information, visit www.us.playstation.com.
Meaning yes, you can play Playstation 1 games, but there may be the oddball title that will give you trouble.