With that in mind here are some of the types of insurance that I think are well worth the money:
Life Insurance - that's a big one. If you die, you want to make sure that your loved ones are well taken care of. However, even here it is important to understand that if you don't have dependents, you probably don't need life insurance.
Disability Insurance - possibly even more important than life insurance (although, I must admit I only have the inadequate coverage offered by my employer). You want to make sure that if you are unable to continue doing your job, you are still able to maintain a decent standard of living.
Home Insurance - unless you are a multi-millionaire (and I mean MULTI), losing your home to a fire or hurricane without insurance could completely devastate your financials.
Health Insurance - if your employer does not offer health insurance, you should make every effort to buy your own. If you can't afford a complete plan, at least get catastrophic coverage with a large deductible, to make sure that you have some backing in case of a major illness.
Car Insurance - we can argue about collision damage, but making sure that you have enough liability coverage is key. Getting sued for all you are worth by someone injured in a collision with you is really something you want to avoid...
There are many other types of good insurance, but the important thing is to understand that what they all have in common is this: they protect you from risks that while relatively small, would devastate you financially if you don't have sufficient coverage.
Now, let's talk about some types of insurance that are useless in my opinion:
Extended Warranties - every time I buy anything at Best Buy, the sales clerks try to convince me to get an extended warranty. But why? Very simply: the company makes money on the policies they sell. Conversely, the cost of the insurance is higher than what they expect to pay me in repair costs. I don't know about you, but if my iPod dies, I don't expect to be devastated financially. Worst case scenario, I'll need to live without portable music for a while.
Life Insurance for Children - your kids do not need life insurance. No one is depending on them for income (unless your child happens to be a famous movie star or fashion model, I guess). If the unthinkable happened and your child passed away, your income would not be effected. In fact, although it is sad to say, your expenses would actually go down. The risk here is not financial, it is emotional, and that cannot be off-set by life insurance.
Vision Coverage - if your employer did not provide vision coverage, would you get it yourself? I wouldn't. Again, the same logic applies: your vision coverage covers the cost of your annual exams and purchasing prescription glasses and such. Most people would probably be better off foregoing the insurance and buying the glasses on their own. Remember - the insurance company needs to make money, so they are charging you more than they expect to pay for your check-ups and prescriptions.
Vacation Insurance - unless we are talking about your dream vacation that you have been saving for for the past decade, insuring your vacation makes very little sense to me. If your vacation gets cancelled for some unforeseen reason, worst case scenario, you get no vacation that year. You are not financially devastated. Your life continues along its normal course.
Again, there are many other types of insurance that do not make economic sense, the common denominator is that even if the worst case scenario occurs, your financial condition is largely unchanged. In such cases, it is best to save your money rather than spending it on buying unimportant coverage.
You can also check out my previous article about buying insurance in your 20's.