The inflation rate for Feb 2013 in the U.S. was 2.0 percent according to Bureau of Labor Statistics reported by http://www.tradingeconomics.com/united-states/inflation-cpi. That is the annual rate projected from the inflation for a given month.
I just got my first quarter savings account statement. The interest rate was 0.1 percent.
In other words, by putting my money in a local bank savings account, I am throwing some of it away. If my account balance was $100 on January 1, then I would gain ten cents in interest but lose two dollars in purchase value by December 31!
Gosh, I remember when I had a savings and loan account in the late seventies, the interest rate was five percent "by law". If you want to make more sense of "by law", see http://en.wikipedia.org/wiki/Savings_and_loan_association. However, even that interest rate didn't cover the inflation rate, which varied from six to fifteen percent from 1977 through 1980.
That was a period of win some, lose some. When inflation was "low", the net loss was "only" a dollar per year. When inflation was high, the net loss was a whopping ten dollars a year.
Your homework is to find some period when savings accounts were a "win" for savings. You might have to dig to get savings account interest rate beyond the last few years.
The only advantage that I see to a bank savings account is being able to walk in the door and withdraw a sum of money for some purchase. It beats borrowing for that purchase. And by paying by check or cash, you're depriving the credit card companies of their rake-offs.