If you are arrested for a DUI 16 years after a previous such arrest, is it considered to be your first or second offense?

What you are thinking about here is, what period of time must pass before a prior DUI is no longer considered in terms of penalties imposed for a DUI conviction.  By virtue of something known as the "look-back period" a prior conviction is not considered in sentencing if it is too old.  For example, in a state with a 5 year look-back period, if you were to have another DUI in year 6, the punishment for the second DUI would be the same as if it were your first. In PA the look back period is 10 years, so since your prior offense is 16 years old, this latest offense will be considered to be your first.

Note: The look-back period only applies for the purposes of imposing a penalty. It still remains on your record.