Other than health and other types of business you typically get as an individual what types of insurance would a business buy?

Some people may need errors and omissions insurance see below:

Why You Need Errors & Omissions Insurance
Regardless of what kind of business you own, customers can claim that something you did on their behalf was done incorrectly, and that this error cost them money or caused them harm in some way.

What Errors & Omissions Insurance Is
In the litigious world we live in today, many business owners protect themselves with errors and omissions insurance (E&O). This type of insurance may be appropriate for anyone who gives advice, makes educated recommendations, designs solutions or represents the needs of others, such as teachers, consultants, software developers, ad copywriters, Web page designers, placement services, telecommunication carriers or inspectors.

How Errors & Omissions Insurance Works
Although formalizing a contract with your clients can help limit your liability, the big expense in an errors and omissions claim is the legal defense needed to prove liability or innocence. Errors & Omissions policies are designed to cover many of these defense costs and ultimately the final judgment if the business owner does not win the case.

I know we had E&O insurance at my former company but I wonder how many small companies have it I suspect not that many.

This may also be more germaine for larger companies but there is also Business interruption insurance. This insurance covers the loss of income resulting from a fire or other catastrophe that disrupts the operation of the business. It can also include the extra expense of operating out of a temporary location.

There is also:

Worker's Compensation Insurance

If your business has employees, worker's compensation insurance will be mandatory. Startup operations typically find that the State Compensation Fund can accommodate your needs. As the business grows, you can then "shop" for better prices for the coverage. In addition, some worker's compensation insurers provide additional services such as risk management and loss control services that may be beneficial to your business operation. These services are typically helpful in holding down claim costs over the long term. Do not confuse risk management with your taking part of the risk. The insurance company should assume 100 percent of the worker's compensation insurance risks.