3 hole outlet on ungrounded line

[Ed Melo]

I have seen some older houses where some of the outlets have been replaced with 3 hole outlets although the line going to them do not have a ground wire.

Is the only good solution to this problem replacement of the wiring?

Would you replace ALL the ungrounded wiring ? I'm sure this could be expensive but is it safe to leave the ungrounded wiring in place?