They could do anything to your computer that you could do. Fortunately, you don't have to let hackers in. Security is a matter of risk management. You can spend between 50 and 1,500 bucks. There are software and hardware products available.
Some Internet providers downplay the risk for home users.
The way we configure our connections, it's very secure. If I was a casual user, I wouldn't worry. Harless leans the other way. There is a real risk out there. Home users are at the same risk.