To keep the roof healthy:

Trim trees and remove dead branches to prevent them from falling due to wind, ice or snow.
Check for roof damage and clean gutters and downspouts–especially important during the fall to keep leaves from building up in gutters.
Consider impact-resistant roofing material if you live in a hail-prone area and are planning to build or replace the roof on your home.
Add extra attic insulation to prevent ice dams. These are caused by excessive heat escaping from a poorly insulated attic, melting ice and snow on the roof and refreezing. This can cause water damage inside the home.
Check flashing to make sure it is in good condition to help prevent water penetration.
Check for and repair surface bubbles and areas with missing gravel on flat roofs, or missing or damaged shingles or tiles on sloped roofs.

Look out below.

After the roof is secure, make sure your basement is in good condition.

Have your furnace cleaned and inspected annually by a qualified technician.
Keep flammable materials, including all lawn and power equipment, away from water heaters and wiring in the basement.
Insulate water pipes in areas exposed to cold temperatures and turn up the thermostat during extra cold periods.

Don't let the outside get in.

Leaky windows and doors can allow rain, snow and cold air to get into the house, which can cause big problems down the road.

Check and repair caulking around doors and windows that show signs of deterioration.
Check caulking around showers, bathtubs, sinks and toilet bases; and make repairs as needed.

Since you're doing the rounds, take a close look at wiring, appliances and any other areas that could cause problems:

Have your chimney professionally cleaned and maintained every year.
Clean and/or replace your furnace filter.
To prevent fires, clean the clothes dryer exhaust duct and space under the dryer. Remove all lint, dust, and pieces of material.
Check your electrical outlets for potential fire hazards such as frayed wires or loose-fitting plugs. Be sure not to overload electrical outlets, fuse boxes, extension cords or any other power service.
Keep a multi-purpose fire extinguisher accessible, filled and ready for operation.
Inspect your smoke detectors. Make sure there is one on each floor of your home. Test them monthly, and change the battery annually or as needed.