You been given good information below, but there is more to consider:
Most homeowner insurance policies do NOT cover the amount you paid for the home. Rather, they will cover the amount necessary to rebuild/replace your home in the event of fire or other damage.
The purchase price of your home includes the land the home sits on. Your insurance will NOT cover the cost of the land, as the land will not be lost in a fire. Often, but not always, the coverage of the home is lower than a recent purchase price. (Assuming you just purchased the home)
Most insurance companies will send an adjuster out to view the home (either an interior or simply an exterior inspection) and then they determine the replacement/rebuild cost of the structures only.
Of course you will also want to consider policy add-ons, such as personal property coverage, liability coverage, etc.
Speak with a qualified insurance agent for more information and specific details for your own situation.
By far the best advice in my opinion has been mentioned by some of the answers already given.... and that is spring for the replacement cost. The dollar difference is not astronomical, especially if you take every precaution recommended by your insurance agent to ensure you receive appropriate credits. I know of all too many cases where people were under insured and regretted their short sightedness. I don't know where you are looking but if you're in the Fairfield county area my broker happens to be an insurance broker also. He would be happy to help you sort out this type of thing. Call the Gabriel Agency at 203 502-5000 and tell him Ted gave you the number.
Replacement Cost. Most Expensive. This will cover the cost to rebuild your home today. Labor, material, and some additional coverages like loss of use will give you a home for the cost it takes to build it today.
Actual Cash Value. Less Expensive. This is exactly like replacement cost except they depreciate the value of the home by the age of the home. A home that is 50 years old my get a 25%-50% reduction in coverage in comparison to a replacement cost policy. Think of it like car insurance. A new car that has collision coverage may pay 20k if it is totaled today and will pay lets say 10k if it is totaled in 5 years. The value of the home or car goes down over time. The problem is you cannot rebuild a home today with that amount of coverage and if you decide to rebuild you will have to cover the depreciation just as you would if you totaled an older car and wanted to replace it with a new one.
Market Value. Less Expensive, Becoming much more popular today. Market value is the value of the home if someone were to buy it today. It will not be enough to rebuild your home but would give you what the house is worth on the open market. This is a great option for investment properties because most investors do not want to wait for a home to rebuild and with the high inventory levels will probably buy another home very quickly and move on with the business of renting properties.
I hope this helps.
The Home Insurance Specialists.