But that doesn't stop insurers falling over themselves to sell a much wider range of "just in case" insurance policies. And if you are the worried type and buy up just about everything going, the costs for an average family can mount up to more than pounds 7,000 a year (see box).
Assuming you have got motor, home and life cover - the most essential insurance for many people - what should you buy next? You need to make a list of your priorities; for many people this might be a policy to protect your income if you are off work for a long time or become disabled.
So how do you decide what is a priority? Peter Staddon, technical services manager at the British Insurance Brokers Association, says: "The biggest investment you make is the purchase of your home, and that needs to be protected. Work out whether you need income replacement insurance.
"Also, a lot of people are under-insured on home insurance as they don't realise the value of their assets."
Under-insurance is often unintentional - you may have taken out a home contents policy several years ago and simply renewed it each year. In the meantime, you have probably acquired a lot more possessions and the value of your jewellery or antiques may have risen sharply.
Most advisers consider life insurance to be an essential buy, and many recommend that you take out enough insurance to cover between five and 10 times your annual household income.
But in fact you don't need life insurance cover unless you have dependents. If you are single and have a mortgage, some lenders insist on life insurance. If yours doesn't, you can bypass this cover if you think that the sale of your home would raise enough cash to repay your outstanding mortgage.
Mr Staddon's favourite little-known tip is legal expenses insurance, which is usually offered as an add-on to home contents insurance or motor insurance. "It only costs pounds 15 or pounds 20 and it gives you the power to take action against others - and you get a free legal advice helpline."
If you do have the money to go beyond core insurance policies, some enterprising firm will have a policy for your individual needs. At the more extreme end of the worry spectrum, Grip, an off-the-wall insurance outfit, offers cover against being converted into a werewolf or a vampire. It also has a special millennium policy.
If you choose to take out this cover, Grip will pay out pounds 5,000 in compensation should you be hospitalised because of alcohol poisoning, arrested or unable to "perform" on New Year's Eve.
HOW MUCH CAN YOU SPEND TO BE SAFE?
These figures are based on an average family living in a four- bedroomed detatched house in Ipswich. The father is a 45-year-old IT consultant and the mother a 45-year-old receptionist. Both are non-smokers. They have three children: a daughter, aged 20, in her second year at Leeds university; a son of 17 who is in full-time education and has just passed his driving test; and another son, aged 10, who is still at junior school.
They have a Ford Mondeo, insured in the father's name and a Renault Clio, which is insured in the mother's name and has the two older children as named drivers. Both have full no-claims bonuses.
House and contents insurance
AXA Insurance: up to pounds 35,000 contents, all risk pounds 119.00
Scottish Amicable: 10-year joint policy, level protection, to pay out pounds 100,000 pounds 552.00
Admiral: 1998 1.8 litre Ford Mondeo, fully comp
for any driver over 25, pounds 100.00 excess pounds 262.00
1995 1.1 litre Renault Clio pounds 512.00
Student house insurance
Saxon Direct: postcode LS2, pounds 2,000 contents cover,
pounds 1,200 extra cover for a computer pounds 105.00
Private health and dental cover
Bupa: local care medical cover pounds 2,591.06
dental cover pounds 661.68
Columbus Direct: annual worldwide family cover pounds 145.00
Pet Plan: pedigree dog pounds 133.20
cat pounds 61.20
Norwich Union: school plan taken out by the
school to protect against injuries and accidents pounds 2.00
Bupa: pounds 605.94
Bupa: pays up to pounds 20,000 for each adult and up
to pounds 15,000 for each child pounds 1,281.68
TOTAL: pounds 7,031.76