More information is needed to provide a comprehensive answer but here's a broad brush overview.
At a minimum, you will want some general liability coverage. You will be in contact with a large number of people and CGL (commercial general liability) coverage will apply if you negligently harm anyone. Given this line of work, the coverage probably doesn't need to be very large. If you are operating as a sole proprietor with no employees and have a homeowner's policy, you should check to see if you are covered under that policy (a long shot but I've seen such coverage in homeowner's policies before).
If you are going to be operating a store front, your lease will probably set forth a number of insurance requirements, such as property coverage for your property and that of your customers. If the lease doesn't require it, you would also want to be sure to have premises liability coverage, which covers slip/fall claims. This might be provided under a CGL policy.
If you're going to be travelling to customer's homes, auto coverage will be needed. Most states already require a minimum level of coverage and your personal coverage may be adequate for you alone. If you're going to have employees travelling to customers' homes, you may need to buy an auto policy in the name of the business (because if the employee gets into an accident on the way to a worksite, the injured party will have a claim against both the emloyee and the business).
If you're going to have employees, you have workers' compensation coverage requirements (most states alllow the owners of a business to opt out of workers' comp).
I am an attorney who negotiates service agreements for a health care client and the above coverages are the minimum types of coverages we generally require of our vendors (specific engagements may call for additional types of coverages). Note that I did not include coverage amounts. These can vary radically depending on the specific service and the locality where you will operate. There may also be state-specific insurance requirements that go beyond what is listed above. I strongly recommend that you speak with a few insurance brokers (definitely shop around). They will know much more about the risks presented by your business, state requirements, and the litigation climate (i.e. what limits you should maintain to adequately protect yourself in the event of a claim).
Finally, insurance is only a product that treats a symptom (i.e. having a claim made against you). It is prudent to actively engage in preventative measures as well. Waivers of liability, if carefully drafted, can be effective in preventing claims (for example, if you destroy data on a machine you are working on). Waivers need to be very specific to the risk involved. Further, many states have very specific requirements for waivers before they will be enforced (and some states don't allow them to be enforced at all). You may want to do a little online research yourself and than confer with an attorney if your budget permits. Customers need to be aware that if they saved 10,000 ancient family photos, their only copies of their tax returns, and the formula for cold fusion on computer they are giving to you to work on because of massive virus problems, there is a very real possibility that the data will be destroyed and that you cannot be held responsible for the consequential damages resulting from such a loss.
Sorry if this sounds a bit daunting. It really isn't and once you take care of the insurance issue at the onset, you generally won't have to worry about it on an ongoing basis. However, this is one area you shouldn't ignore. A single claim can really screw things up for you.
