How can I save on homeowners insurance?

Where do you live?
Major metropolitan areas like New York, Chicago, San Francisco and Los Angeles among others, are hot spots for crime. Thus, your premiums will be higher. Suburbs of major cities tend to have lower homeowners insurance rates than within the metro areas. If you live in a rural area and your home is more than 500 feet from a fire hydrant, your home insurance rates will be higher. In addition, rates vary widely from state to state. Florida and other states prone to hurricanes have significantly higher home owners insurance rates. The same is true of homes located in areas prone to earthquakes.
You could change where you live, but it's an expensive way to reduce your homeowners insurance premium. If, however, you live in a major metropolitan area, adding things like a burgler alarm, security doors or window bars could mean lower premiums. If you're on acreage in a rural setting, adding a water storage tank on the property could lower your premiums. For those living in hurricane or earthquake zones, you might want to hurricane-proof your home or earthquake-proof your home.

What kind of home do you live in?
It stands to reason that the more a home costs, the more it costs to insure. You're not going to sell you home just to save on homeowners insurance. Homes built in the early part of the 20th century cost more to insure than newer homes since these homes typically cost more to repair or replace.
Your existing home may cost less to insure if you add simple things like a fire extinguisher, smoke alarm or dead-bolt locks. If you can afford a luxury home, it might pay you to install a sprinkler system and a fire/burglar alarm system. Older homes may benefit from rewiring and replumbing.

What is you credit score?
It didn't used to be that credit scores were used in determining homeowner insurance premiums. Now, in many states, your risk quotient is determined in part by your credit score. Actuaries have determined that the lower a credit score, the higher the insurance risk. Those with "excellent" credit will have a FICO (credit) score of over 720. A score between 680 and 719 is average and still considered an acceptable risk. By the time you start dropping below 680, you start to become an insurance risk. The lower the score, the higher the risk and the higher your insurance premium. It's a good idea to check your credit score a minimum of once a year. By law, you can receive one report a year FREE.  If you want or need a report more frequently, as when you are trying to improve your credit score and want to keep tabs on it, you will have to pay for it.
Your credit score is something you can change. First of all, never miss a payment on your rent, mortgage, credit cards, etc. Make sure your payments are always made on time. One 30-day late car payment can lower your credit score by 100 points.  Keep credit card debt at less than 50% of your high credit limit. For example, if your high credit limit on a card is $5000, you should never charge more than $2500 on that card. These three simple steps can go a long way towards restoring and/or maintaining good credit.

How much is your home insured for?
It's amazing how many people over-insure their homes. This usually happens for two reasons:

First, lenders often require home owner insurance in an amount equal to the loan amount. This is find if the equity in your property equals or is greater than 20%. Lenders only insure the value of the improvements (structures) on the property, not the land itself. They deem the value of the land to be roughly 20 - 25% of the value of the whole. In other words, if your home appraises for $200,000, the land value is $40,000 - $50,000, and the value of the home is $150,000 - $160,000. Land is indestructible (99% of the time), and should never be included in the insurable value.
If you secured a mortgage with less than 20% down, you do not yet have 20% equity in your home, and your lender required insurance in the amount of the mortgage, you may be able to negotiate with your lender to reduce the coverage amount to a more reasonable level  thus reducing your premium.

Second, most homeowner insurance policies today contain an inflation clause that increases your coverage every year to keep up with inflation, usually 2 -4%. This has a compounding effect which, over time, can cause the amount of coverage to exceed the actual replacement cost.
It's important to review your homeowners policy no less than every five years to determine adequate coverage. There's no sense paying for coverage that you will never use.

Many times you may feel that the insured value of your home is too high based on what you paid for it. Insured value is based on what it would cost to replace the home in today's market -- not what you paid for the home. Also, it is infinitely more expensive to restore a home damaged by water or fire than it is to rebuild the same home from the ground up. Thus, there may be a wide spread between the cost of the home and it's insurable value.

Deductibles.
A deductible applies to the property portion of your insurance policy. The cost to repair your home in the event of a loss will be paid less whatever deductible you choose.
Deductibles do have a bearing on your premiiums. The higher the deductible, the lower the premium.  Choose your deductibles based on how much you can afford to pay out of pocket to have your home or personal property repaired or replaced should you have a loss.

Claims.
No claims means lower premiums and the longer you remain claim-free, some companies offer further discounts. One small claim may or may not raise your rates depending on the insurance company. Two claims, usually no matter what they're for, will most certainly raise your rates. Two major claims will, no doubt, get your policy cancelled. 
You say, "Claims are why I pay for insurance." Not really. You pay insurance for peace of mind, just in case you ever have a claim to file or someone files a claim against you. You pay for health insurance because the cost of being sick is too great to pay out of pocket, but you don't plan to ever be sick. Think of homeowners insurance the same way. In fact, think of any insurance this way. So what can you do to avoid claims? Above all, don't use your homeowners insurance policy as a maintenance policy filing a claim for every small thing that happens like a broken window or other minor damages. Choosing a high deductible can help eliminate this temptation. If you have a dog that is prone to biting someone, keep the dog away from everyone but immediate household members. Your insurance company may pay for one dog bite, but they won't pay for two. Make sure your property is free from trip-and-fall hazards like big cracks in sidewalks, loose handrails on stairways, rugs that don't lay flat, objects strewn around that could easily cause a mishap if not seen, guns that are not safely locked away, etc.