Life insurance: If there is someone is relying on your income, you need life insurance.
Your wife should also be insured, even if she doesn't work. The need to insure her comes from the expenses of replacing her for childcare and housework. And if she does work (or is the breadwinner), then you need to insure her for income replacement - don’t be too macho to insure her.
How much to get?First figure out how much you live on for real.
One school of thought is to get enough life insurance that you don't use up that payout, only live on the income that money generates. So to make $80,000 of income at 5%, you need an initial investment (insurance amount) of $1,600,000 or over 1.5 million dollars! This piece of advice makes very little sense in today's low interest rate environment - since to chase a 5% return you need to risk the principal.
A better plan would be to estimate how many years of income replacement or expense coverage you need for each spouse. A big part of the need for income comes from child related expenses, which will end after the children reach a certain age. Or, at younger ages it is reasonable to expect that a widow/widower could get remarried, and therefore won't need as many years. Take all this into consideration and consult a financial adviser if you can afford it.
Another plan. She'll be able to go to school, or otherwise get set up for a high paying job with a few years of full support. So you only need a few years’ worth of income. Let's say $80,000 X 5 years = $400,000. Realize that her expenses without a husband might be higher than now as a couple. (babysitter, tutors, etc)
Term insurance vs Whole life Term insurance is the cheapest and simplest. You pay a premium and if chv”sh the insured person dies, the beneficiary gets the insurance amount. The higher the risk a person is, the higher the premium. So people with worse health will pay more than healthy people for the same amount of insurance, and older people will pay more than younger people.
Level term. One popular type of term insurance has a level premium for a fixed number of years. Many people prefer this to the traditional type of term insurance where the premium each each year pays for coverage only in that year (and as a result the premiums increase every year, because you are aging). In contrast, a level premium term insurance policy has an unchanging premium amount that is guaranteed for a specific number of years. As a result of the design you are overpaying in the early years of the policy to subsidize your cost in the later years. Popular guarantee periods are 10, 20 or 30 years. As with any insurance, it pays to get one while you are healthy to lock in the lowest rate possible (in general, health only declines, you rarely hear of people getting healthier with age).
Whole life has a level premium that is guaranteed not to increase for as long as you live. Because of insurance laws in the US, this type of insurance policy must always have a "cash value", which is the amount of money you get back if you cancel the policy. That makes Whole Life a much more expensive choice relative to pure insurance coverage (where you'd get nothing back if you cancel) and therefore a bad choice for most people who are not rich (this is complicated to explain in great detail, but it is an effective summary of who is most likely to see good value in buying Whole Life). One fringe benefit of having a cash value in Whole Life is that you have saved money which can be used for your retirement or any other purpose if you are still alive. For most people though, other savings vehicles will be better.
Universal life is very similar to whole life, in that it is meant to provide insurance coverage for as long as you live (as opposed to Term, which is meant to for a short to medium period of time). The most important difference is that the premium rates for Universal Life are not guaranteed, unlike Whole Life which is completely guaranteed. The concept behind Universal Life is that the insurance company tells you all the charges you are paying for and lets you pay as much or as little as you want for the coverage. Anything extra that you pay goes into an account that can earn interest, and as long as that account doesn't run out of money you stay insured.
Variable Life is an offshoot of Universal Life. The difference is that instead of the extra money going into an account that earns interest, you can choose to invest the extra money in mutual funds. Take my word as an expert in insurance that Variable Universal Life is only for the most investment oriented people (meaning that they barely care at all about the insurance part of the policy). If you are trying to decide on Term or Variable, the answer is always Term.
How long a Term Insurance companies make tons of money on people who buy 30 year terms and then let it lapse after 10 years, since they paid 30 year rates for those 10 years. Consider a long term Term the equivalent of insuring against the possibility you will be uninsurable in 10 years. Consider also that you would be able to convert the short term Term into a whole life policy at that time regardless of insurability.
Life insurance has some very favorable tax treatment on the cash value (or account value), which is a big selling point, especially for people in certain tax brackets who have all but run out of tax advantaged places to save money. The exact details are very technical and could not be fairly explained without making this wiki extremely long.
Reevaluate your situation and the amount of insurance periodically. As things change- income, spending, family additions- the amount of coverage you need will need tweaking.
In addition to buying insurance, don't forget to set up plans for how your beneficiaries can use the insurance money to live with their needs taken care of. Providing for your family in case of a tragic event is perhaps as selfless an act as a person can do, don't do it halfway! Make sure there will be money AND a plan for how to live on it. In my experience I have seen all types of unqualified people get involved with "helping" a family live off huge amounts of money and getting it wrong 10 times out of 10.
Plan for guardians to care for your children if cv"sh both parents are unavailable.