If one of your New Year's resolutions is to grow your savings, one smart strategy is to keep your money in an account earning the most interest.The Federal Reserve has been slow to raise interest rates, and even recent hikes haven't trickled down to consumers in the form of better savings yields. The average savings account offers a paltry 0.19% annual return, only slightly better than a year ago, according to Deposit Accounts.Some experts say that money could grow faster at online banks. Some CDs, or certificates of deposit, are also more generous than others."If you're not seeking out the best returns on savings accounts and CDs, you're leaving money on the table," said Greg McBride, chief financial analyst at Bankrate.com. "It's the only place in the investment universe where you can get extra returns without extra risks."These accounts are protected by the Federal Deposit Insurance Corporation, a government agency that provides deposit insurance, for up to $250,000.Savings accountsOnline banks, McBride said, are currently in an "arms race" to lure people with the best rates.Although current "best" rates of around 1.5% still seem low — one could find savings accounts with a 4% annual percentage yield in 2006 — experts say they make sense in the current environment."We had record low interest rates for nearly a decade, and inflation is still 1.6%," McBride said. "When banks are giving car loans for 3% and mortgages for 4%, no one is getting 10% on savings."People are also less likely to look to the past than they are to compare today's rates against each other, said Patricia Seaman, senior director of marketing and communications at the National Endowment for Financial Education."People feel good about saving 5 cents a gallon on gas, so they feel better about getting another half a percentage [on their savings]," she said. "We may not be talking about very much, but psychologically, that looks amazing."Here are some of the banks with the best savings yields:1) Dollar Savings Direct, a division of Emigrant Bank, claims to have "America's highest rate." Saving accounts come with an annual interest rate of 1.60%."It's a smaller Internet bank, but it's still a legitimate, FDIC [Federal Deposit Insurance Corporation] insured bank," said Ken Tumin, founder of the website DepositAccounts.com.2) Marcus by Goldman Sachs offers online savings accounts with an annual interest rate of 1.40%. "Goldman Sachs seems to be a little hungrier for deposits," McBride said. First National Bank of Omaha also offers an annual interest rate of 1.40% on a savers' online account. Neither requires a minimum deposit.3) American Express's savings accounts accrue at 1.35% a year.4) Discover online savings accounts come with a 1.30% annual interest rate. In this account, $15,000 would produce a return of $194.74 in a year. To compare, that same amount in a Chase savings account would earn just $1.50. Barclays, too, offers an online savings account with an interest rate of 1.30%.5) Synchrony Bank offers a savings account with a 1.30% annual return — and its accounts come with an optional ATM card, although like with most online savings accounts, there is a limit of six withdrawals or transfers in a month. Although this restriction might feel like a nuisance, it's actually helpful to people, McBride said."Too easy access can defeat the purpose of saving," he said.Certificates of depositFor savers who won't need their money for an extended period of time, interest rates on CDs can be worth a look. The average 1-year CD returns 0.28%. Rates from online banks, however, are also higher.People generally can withdraw their CD interest at any time throughout the term. There are penalties for withdrawing the original deposit."If it helps you to think, 'I can't get that money', it's worth it," said Seaman.Here are some CDs with the best rates:1) Online bank Ally has one-year CDs that range from 1.35% to 1.70%, depending on how much is deposited. Savers should look for CDs with the lowest penalties, said Allan Roth, founder of Wealth Logic. That way they can gain the benefit of a high interest savings account without the restrictions of a CD. "If you need the money, you break the CD," he said.2) Marcus by Goldman Sachs also offers certificates of deposits with higher-than-average returns, although there is a $500 minimum deposit. A one-year CD comes with a 1.65% interest rate, and a six-year CD has a 2.55 percent annual rate.3) Barclays offers a 1.65% return for one-year CDs; five-year CDs will deliver 2.40 percent and there is no minimum opening deposit.Savers can also "ladder" their CDs, in which a person deposits money into, say, a one-, two- and three-year CD, so that they're not tying up too much of their money at once and can reinvest their savings should rates rise.It can be hard for people to spend the time and energy to change their saving ways, Roth said. People need to "fight that inertia.""I know so many people that will complain about a sandwich being $12 when it should be $10," he said. "And yet they lose thousands of dollars each year by having their money in a big-name checking account."Keep in mind you'll pay ordinary income tax rates on earnings from savings accounts.