Who needs life insurance? Advice to young adults

As long as you each are able to support yourselves and you have no kids (and no mortgage) you don't need life insurance. Very few young adults become uninsurable. Note that one company might deny coverage while another company will sell the same person a policy. See: http://wealthpilgrim.com/who-should-buy-guaranteed-issue-life-insurance-a-surprising-answer/ (note the author is a certified financial planner which lends credibility).

How do I guarantee future insurability with a term policy? http://www.fool.com/insurancecenter/life/life08.htm

What factors might supplement replacement income? http://www.fool.com/insurancecenter/life/life03.htm

Note the important role Social Security plays in replacing income. Early in my career I had a student who was a widow with 4 kids under the age of 6. Her husband was killed in a vehicle accident when they had 2 toddlers and she was pregnant with twins! They had no life insurance. Luckily he had worked long enough to be covered by SS so she and the kids received SS survivors’ benefits. Very few insurance sales people will even mention SS Survivors' benefits as part of the process of deciding if you need insurance and, if so, how much.

SS Survivors Benefits http://www.socialsecurity.gov/pubs/EN-05-10084.pdf  "The younger you are, the fewer years you need to work. But no one needs more than 10 years of work to be eligible for any Social Security benefit. Under a special rule, if you have worked for only one and one-half years in the three years just before your death, benefits can be paid to your children and your spouse who is caring for the children." Each of you should set up an online Social Security account: http://ssa.gov/myaccount/

If you decide to buy life insurance read:

Life Insurance Buyer's Guide (but note the publisher is the industry) http://www.naic.org/documents/consumer_guide_life.pdf

Consumer Reports article: http://www.consumerreports.org/cro/money/insurance/life/life-insurance-safety/how-to-protect-yourself/life-insurance-safety-how-to-protect-yourself.htm

New York State Life insurance consumer info: http://www.dfs.ny.gov/consumer/clife.htm

Do either of you have life insurance as an employee benefit? Sometimes you may have 1x your annual salary in insurance as a free benefit. Can you buy cheap life insurance as an employee benefit? By buying through your employer you are part of a group plan which does not require a health check (or only if you want to buy a really high amount of coverage).

Also consider that the surviving spouse would be the beneficiary of retirement accounts and other assets.

If you had a mortgage that you need both incomes to pay and want to be sure the surviving spouse could afford the mortgage if one of you died, then you might want to buy term life insurance policies.

Life insurance salespeople use scare tactics to try to sell guaranteed renewable whole life insurance because they earn much higher commissions on whole life policies than on term policies, not only when they first sell you the policy but for years afterwards if you keep paying premiums. So the sales person will really push whole life. 
You might be better off funding Roth IRAs.