If I'm re-entering the US via a POE that I don't normally use, such as HNL (stamp is "HHW") I'll ask for a stamp if they don't stamp it automatically.

If I'm making a routine re-entry at ORD (CHI), DTW (DMA), ATL or LAX, I don't care if they stamp or not.

Sometimes I will ask for a stamp if I there is doubt regarding my exit from a nation. I don't see Schengen Zone (EU) as very strict, but case in point:

Enter Schengen via flight from UK -- scanned / stamped in.
Exit Schengen via flight to UK -- flight leaves from schengen gate (no exit control).
Most times - Exit Schengen via flight to UK or USA with full exit scan/stamp.

Above has never been an issue, but best to keep a travel record.

Other case: fly into nation A, go through full formalities -- exit A via land border to nation B with little to no formalities; fly out of nation B with no exit control to a "regional airport" and enter C with few formalities. Depart country C at major Intll Airport with full formalities. Country C confused how I entered at exit control.

Arrive back to nation A at a later date and immigration computer indicates I never left.

Sometimes it doesn't hurt to keep a record.