"Gordon Shumway" wrote in message
under the cabinets. My question is should I leave the cabinets in
place, along with the old floor, and put a new subfloor and tile over
the existing floor? Or should I remove the base cabinets old floor
and old subfloor, and put a new subfloor and tile from wall to wall
and reinstall the cabinets?

At the very least, take it down to whatever goes from wall to wall
underneath the cabinets. At that point you can decide if sub floor
reconstruction needs to be done. Redoing a floor just up to existing
cabinets is leaving yourself open to a whole lot of future cursing,
swearing, misery and burning of money.

That is of course unless you're planning on moving soon and don't care that
you'd be passing all the future cursing, swearing, misery and burning of
money onto someone else.