I'm 29, single, and healthy, with the hopes of someday--ideally within the next few years--getting married. Do I need life insurance? For what it's worth my employer pays a small policy that would give the equivalent of one year's salary in the event of my death--more than enough to cover any funeral costs.
The purpose of life insurance is normally to protect your dependents in the event of your death. Since you don't have any dependents, I would say you don't need life insurance. (See this question for a fuller answer).
However, you may choose to buy life insurance now on the basis that you hope to have dependents in the future, and depending on your circumstances at the time it may be more expensive to buy life insurance then than it is now (for example if you are diagnosed with something like Type II diabetes or heart disease in the interim).
You can also buy life insurance as an investment though I would advise against it; see this question for how this works.
One thing that came to my mind is, has anyone ever co-signed a loan with you? Perhaps private student loans, or a credit card (even the lease on your apartment)? If so, then you will need to ensure that those debts will be settled in the event of your untimely death, because if you die, your co-signer becomes fully and solely responsible for it. You don't need to worry about federally-backed student loans and certain other types of debt; in the U.S. at least, these are discharged if the student dies, with or without a co-signer. However, most "private" debt such as car notes, credit cards, private education loans, etc will not be discharged with your death if there is another signature on the paperwork.
The basic idea is that you name someone in the insurance paperwork as your beneficiary, who will receive the direct payment from the company in the event of your death. This payment is usually not subject to claim by creditors, because it was never part of your net worth as of your death, and therefore isn't included in your estate. You can, however, direct that the beneficiary, as "executor" of that money, make specified payments to other people who have co-signed loans with you, in the amount of any outstanding balance on said loan.
For any sort of estate planning, I would recommend you consult a lawyer. Most estate lawyers work relatively cheap as opposed to those in other areas of civil law, and many will at least waive their hourly rate for the initial consultation. Having a lawyer consult with you and draw up the document helps ensure that you aren't forgetting anything, or that an unwitting error or omission in language doesn't render the document unenforceable or pervert its intentions. Once it's drawn up, you simply review it, and then sign it in the presence of a notary public who will witness and seal it. From this point, that document should be as good as your own word on the stand should anyone try to challenge it. If you ever need to change it (and you will), you simply repeat the process; the most recently signed and notarized will supersedes all others.