It’s rare to ride down Suffolk’s rural roads in autumn and not spot a deer — or three — grazing or darting across the fields.

Though I’m used to keeping an eye out for the graceful creatures, I never saw the doe that bounded across Godwin Boulevard in front of my car on Oct. 8 — until it was too late. The deer hit the front end of my car, causing an estimated $3,900 in damage to the car.

Accidents between deer and vehicles are becoming increasingly commonplace in Virginia and around the country, according to insurance statistics.

The number of deer-vehicle accidents in Virginia is up nearly 32 percent since 2003, according to a State Farm Insurance study. Earlier this week, the company issued a report showing that 54,135 Virginia drivers — one in 123 — hit a deer during the last half of 2007 and first half of 2008.

Virginia ranks eighth nationwide in the number of motorists involved in deer collisions, according to Drive Smart Virginia, a non-profit funded through the automotive insurance industry. The state with the most collisions, for the second year running, was West Virginia.

The organization urged drivers to use extra caution over the next couple of months, which is breeding season for the whitetail deer.

“We want Virginia’s drivers to be aware of the potential of deer crashes during the months of October, November and December,” said Janet Brooking, executive director of Drive Smart Virginia.

Brooking said deer ­— male and female — are especially unaware of vehicles on the roadways when their animal instincts come into play. This time of year, she said, the movements increase — particularly around dusk and early evening and pre-dawn to mid-morning — as the creatures search for food and members of the opposite sex.

“More drivers are on the road at dawn and dusk, the very time of day when deer are most active,” said Ray Palermo, director of public relations for Response Insurance, a national car insurer. “A car striking a 200-pound adult deer can not only result in the death of the deer, but also incur an average of $2,000 in damage to the vehicle.”

Response Insurance and Drive Safe Virginia issued the following tips to help motorists avoid hitting deer:

Keep headlights on high-beam as much as possible at night, unless another vehicle is approaching, and keep a close lookout in the fields and woods near the road.

Remember that deer usually travel in herds. If you see one, there are likely to be others nearby.

Do not rely on car-mounted deer whistles. They don’t work.

Don’t swerve to miss a deer. You could lose control of your vehicle, strike a tree or ditch bank and overturn, or strike another vehicle. Fatal crashes or injuries during crashes are rare when just a deer is struck.

Slow down when approaching a deer standing near the side of a road, and be prepared. If startled, the deer can bolt onto the road and into your path. If necessary, honk your horn and flash your lights to try to scare it away.

Take deer-crossing signs seriously, particularly those installed specifically for this time of year. Be particularly cautious in wooded and agricultural areas, where there is little distance between the road and the woods.

If you strike a deer, call police as soon as possible.