On the flip side, naturally degrading health can also be a costly concern for retirees, pushing up the need for expensive long-term care. The average cost for a private room at a nursing home is a whopping $91,250 a year — and that is expected to rise 4 percent annually for the next five years, according to Genworth's 2015 cost of care survey.
Even healthy people can expect to spend a lot on health care in retirement. According to health-care-cost research firm HealthView Services, the average healthy 65-year-old couple that retired in 2015 and is covered by Medicare parts B, D and a supplemental insurance policy will pay $394,954 for premiums, dental, vision, copays and all out-of-pocket costs over the course of their retirement.
With all these financial pressures, it's no wonder people were thinking of raising their savings as they watched the ball drop. But how can they be sure to stick to their resolutions?
Read More Making your money resolutions stick
"The most important piece is to make it as easy possible," said New York City-based financial planner Stacy Francis. "Automatic savings is really the key."
She recommends the first stop for retirement savings be your company's 401(k), to which your contributions can be automatically deducted from your paycheck. Next, consider saving in an individual retirement account and setting up regular payments to it from your checking account.
In 2016, the maximum you can contribute to a 401(k) is $18,000, plus an extra $6,000 if you're age 50 or older, and you can contribute up to $5,500 to an IRA, or $6,500 if you're age 50 or older.
If you can save more than those maximums, Francis recommends next saving for retirement in a taxable account that is not easy to access, like a general brokerage account, for example, so you don't get tempted to spend those funds before you retire.
Another way to ensure you follow through on your resolutions to save more all year long is to regularly review your finances—which is the second-most popular resolution, anyway.
Both Francis and Alderson meet with their clients on a quarterly basis. Francis likes to go over her clients' financials with a custom map. "They can visually see their goals and progress, which makes [their finances] much more tangible," she said. "Most of our clients like to be able to check things off and get that rush of accomplishment."
Regardless of whether you work with a professional, Francis suggests scheduling when you'll go over your finances ahead of time and teaming up with a friend to help motivate you. If you're married, you can make financial dates with your partner. If you're single, she recommends finding a "finance buddy."
"Having that accountability partner, you're going to show up. You may not do that for yourself," she said. "It's the same as running buddies."
Just be sure not to go overboard with your reviews. Obsessively checking your portfolio and following market movements may cause you to trade hyperactively and overreact to the news of the day. "This unhealthy behavior will do nothing for you in the long run except lead you to make really dangerous decisions with your portfolio," Francis said.