I guess I'm somewhat confused by "can I". There is certainly no law stating that you have to replace it.

12AWG is good for 20A circuits, 14AWG for 15A circuits.

If it's truly in good condition and includes a ground conductor, I see no need to replace it.

There is no reason to change those cables. The only reason to replace cables is to get a ground or the cables are damaged. Your's has a ground. Are they damaged? The wire guage has not changed. The old cables can carry the same current as the new ones.

If the old wire is undamaged then there is no need to replace it unless you want to move the wire to a different place such as through the wall studs instead of stapled to the bottom of the floor joists.

The only problem you might have that I can think of is if the old wiring is rated for 70 deg C temp and you want to install light fixtures that require 90 deg C wiring. Even then, there are ways round that problem.

The problem of the temperature rating of the wire is discussed in this thread:

Here is a link that might be useful: Minimum 90°C Supply Conductors

From 1959, the equipment grounding conductor probably is 16 gauge. A bit fragile while wrestling the other conductors into the box along with a device. But I know of no other compelling reason to replace that cable.