How do I level the base cabinets in my 100 year old house?

I would guess that the hose has settled and the floors are no longer level. The best way (most labor) would be to remove and re-install them such that the tops are at the same height and level based on the high point of the floor. Shims are used to get everything level when screwing cabinets to the wall. Then base trim will be used to hide the gaps.

However, I might just try removing countertop and shimming the top to be level. Draw a level line on the wall and shim countertop to that elevation. Countertops normally are 1.5" wide on front and 3/4" sub-base. The front overhang may to enough to hide gaps at cabinet top.

You can purchase shims at your local hardware store. Once you have the cabinets level then install a baseboard to cover the gaps.

Frank,

This could be very difficult depending on how your current cabinetry is secured. You are fighting your countertops, which you need to make sure are raised in unison with the cabinets or they will crack or pop loose from the cabinets, which they are most likely secured to as well as any appliances whose clearance might be affected with a change in the cabinets. If your countertops have an integrated backsplash, that will need to be separated from the wall. The cabinets are also probably screwed into the studs or a cleat that sits behind your cabinets. They are also probably screwed to the cabinet on either side. Those screws or nails may be hidden by putty and paint. You would also have to remove the toe kick panel where the cabinet meets the floor so you can get under them and level them. Instead or leveling the cabinets, I might be inclined to level just the countertops. You will need to determine how they are secured to the cabinets and hopefully they were not secured with construction adhesive. If you are able to free the counter tops, you can shim them so they are level and re-secure them.

If you are talking about a new install use the shims. If this is to "fix" existing heed Seth. If you have stone counters get a professional to do it.