There are two major types of insurance that people carry for their cars - liabiliy and casualty. Liability is for damage that you cause to other people or property with your vehicle, and the damage done by a bicycle is typically so small, that it is not really worth worrying about - your homeowners or renters insurance policy will generally cover you for this sort of damage.

In terms of casualty insurance, this would pay to repair or replace your bike if it were damaged in an accident - again, in most cases, the cost of a bicycle repair is so small, it wouldn't make sense to insure it.

If you are dependent on your bike to get to/from work (as I am), the best insurance is a spare bike. Need not cost much, and this way if you hop on your bike in the morning and find that it is not ridable for whatever reason, you just get on the spare bike. A spare bike can cost as little as the spare tire for an automobile.