I often find homes built on hillsides as a home inspector in St Louis County and St Charles, MO. Controlling and / or diverting storm water runoff is very important on this type of property.
Often, the hill is guiding rain towards the overhead garage door, down a driveway. A drain may be installed in a low spot just before the door, but type of drains are prone to leaf and other debris coverage, pooling, and diversion of the storm water directly to the garage or home.
Negative grade to foundation is common, when storm water prefers to sit and settle near the home, rather than further away in the yard. Drain tile can help, and of course adding dirt along the foundation, to create a downhill slope away from the home is the goal whenever possible.
Landscape retaining walls, while popular and mostly for cosmetic appeal, can catch and trap storm water runoff against the foundation.
Any water trapped in / between soil and the foundation can effect the wall, especially through freeze thaw cycles, which can literally push the wall in, creating new cracks and leaks.
Occasionally, downspouts are attached to damaged buried piping, and actually concentrate roof water directly to the spot you least want it, the foundation.
Sump pump extensions are worth mentioning here as well, as I have regularly seen pumps discharging so close to the foundation, it creates a circulating pump cycle, pumping the same water from under the home, to next to the home, and right back to the pump pit, time and again. While hillside homes are common, knowledge of how to best manage the storm water run off is not. It's a good idea to ensure that it's at least something you are thinking about while home shopping, landscaping, or troubleshooting foundation issues.
Kevin Dickherber Home Inspector St Louis and St Charles, MO