The problems usually involve (1) not using high quality [hardened steel) screw driver bits and (2) the screw is not a true Phillips. There are several variations on the Phillips one of which has a shallower recess (usually found in VCRs/electronics equipment) and requires a slightly different driver tip. The most common type are the Japanese "cross-slot" and require an appropriate screwdriver for removal. These resemble the familiar Phillips. Usually a regular Phillips driver will work, but there is a tiny microscopic difference in the shape also of the cross in the screw head and, as a result, the driver made especially for these screws grips much better than do the standard Phillips. Often a standard Phillips tip can be ground down to make a suitable fit. If you have stripped the slots, then the best bet is to use an appropriate fine steel twist drill to deepen the hole/recess in the screw head and then attempt to turn the screw using a suitable sized high quality Phillips driver but using high forcing pressure to the degree that the driver bit literally bites/cuts (new slots) into the screw head.
I found that this works more often than not.