We tend to get the left-overs of big storms here, and that usually means lots of rain, snow, ice, hail, and higher than usual winds. Other than dealing with a power out bug-in scenario, our biggest concerns are flooding, roof damage and damage from downed trees. Our storm specific preps include:

Keeping stuff off the basement floor in shelving or in Rubbermaid bins
A pump for the basement
Plastic sheeting, duct tape, lumber, nails, tools, etc. to do repairs
Storing outside stuff securely so it doesn't become projectiles
Keeping the trees trimmed
Lots of battery/flame lighting
Lots of blankets
Helmets, safety glasses, safety vests and work gloves for outside work during a storm (ie - clearing the storm drains)
Shovels, axes, saws, buckets
Crank/solar radio
Preps on all floors and rooms in the house, including the usual suspects in terms of bugging in (I.e. BBQ, Coleman propane stove, extra propane, lots of water stored, full pantry and deep freezer, etc.)
Family BOBs ready to go (half stored in the family BOB)
No less than half a tank if gas in vehicles

Bugging out is our last option, especially now with a baby, but we're working on our mobility.

Forgot some important ones that we do as the seasons change - fresh batteries in all the smoke and CO2 detectors, clearing any debris from the dryer vent, cleaning the eaves and fixing the stupid one on the front corner of the house that blows out every spring.