Dan,
In general, one should consider purchasing life insurance when there is a current or soon-to-be-anticipated financial need. A financial need for life insurance means, in effect, that someone would be FINANCIALLY adversely impacted if you were to pass away.
In the overwhelming majority of cases, the first purchase of life insurance occurs when a couple is having children (either when they are planning to get pregnant, when the couple just got pregnant, or when children were recently born). Almost by definition, having children means you have other people who are financially dependent on you, and thus would be financially impacted if you were to pass away.
In some cases, couples also purchase life insurance even without having children involved, simply because their lives have become so financially co-dependent. For instance, if one individual's income primarily supports the couple and maintains the current standard of living, insurance may be appropriate to allow a surviving spouse to continue that standard of living in the event of an untimely death. However, it's worth noting that for many couples, particularly when they are younger and still don't have children, life insurance is often less necessary, because the reality is that both members of the couple may be capable of separately supporting themselves if necessary if there was a divorce.
There are some other reasons for life insurance as well, associated with businesses, and with managing estate taxes, but those situations would merit a separate discussion.
At the end of the day, life insurance represents a trade-off - to pay a portion of your current income to manage the financial impact of a potential untimely death. Even individual and couple will make their own decision about whether/when to engage in that trade-off, depending on their own personal goals. But to say the least, if someone really IS financially dependent on your income, consider protecting them!
I hope that helps a little!