Online banks, McBride said, are currently in an "arms race" to lure people with the best rates.
Although current "best" rates of around 1.5 percent still seem low — one could find savings accounts with a 4 percent 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 percent," McBride said. "When banks are giving car loans for 3 percent and mortgages for 4 percent, no one is getting 10 percent 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 percent.
"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 percent. "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 percent on a savers' online account. Neither requires a minimum deposit.
3) American Express's savings accounts accrue at 1.35 percent a year.
4) Discover online savings accounts come with a 1.30 percent 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 percent.
5) Synchrony Bank offers a savings account with a 1.30 percent 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.