In most cases, your insurance company should cover it. But, two things: One is the loss of use mentioned a couple of times above. I had an accident with an Alamo car out in Nevada several years ago and my insurance company handled most of it. I did have to pay for a few days of "loss of use". I thought that was going to be a big problem, but I felt Alamo was very fair about it. I think they charged me for about 3 days and the rate they used was quite reasonable...less than a 3 day rental would have been. The other thing about using your own insurance company is that an accident with a rental does count when computing rates. Usually with one accident, that shouldn't be much of an issue, but if you have more than one in a given period, it could.
What I've done lately is use a program that American Express has where they charge about $30 per rental, regardless of the rental length, and they cover everything including loss of use. Unless your rental is only a day or two, it is much less expensive than the insurance offered by the rental agencies.