* The Firstar Bank in Appleton, Wis., offers its customers a non-interest-bearing checking account with no minimum-balance requirements. There is, however, a $2-a-month fee for the account and a 20-cent-per-check fee if more than 15 checks a month are written.
* If you can keep $300 in a regular checking account at the Vermont National Bank in Brattleboro, your checking is free. If you are ''60 years young'' or older, you don't even need the minimum balance.
* Customers at the Wilmington (Del.) Trust Company can have a checking account with no minimum balance and no service charge if they agree to use automated teller machines (ATM) instead of human tellers. If these customers do use a human teller for deposits, check-cashing, or account inquiries, there is a
* People who want to sign up for the ''Special Plan'' at First Security Bank & Trust Company in Lexington, Ky., pay a flat $3-a-month fee for their accounts. Each customer is given a Visa debit card, which also serves as an ATM card. All ATM transactions are free, but checks cost 20 cents apiece.
* Security Pacific National Bank in Los Angeles allows its customers to see a live teller only twice a month without paying a fee for it.
In the banking industry, these are examples of ''no-frills checking.'' For the banks' customers, they are a sometimes confusing replacement for the free and easy-to-comprehend checking accounts they used for decades. Those accounts, however, have almost all gone the way of green eyeshades and sleeve garters: They just don't fit in the picture of the modern, less-regulated bank anymore.
Ironically, the spread of no-frills checking seems only to have increased the debate about banking deregulation and how it affects individual consumers. Particular concern has focused on the elderly, those living on low and fixed incomes, young people, and anyone else who does not have thousands of dollars to establish the sort of ''relationship'' with a bank that would eliminate charges on checking accounts and other basic transaction services.
It is in part because of these concerns that banks have come up with various forms of no-frills checking and special accounts that carry few if any charges, as long as the customer follows a few rules, like using only an ATM.
Banks are also adding various ''lifeline banking'' programs aimed at providing basic banking services to the poor and elderly, and perhaps the young, too.
''A large number of banks are looking at lifeline accounts,'' observes John Kneen, a manager at Cresap, McCormick & Paget, a management consulting firm.
''You can see lifeline banking as very much like utilities that are required to keep the heat on for poor people in the winter,'' says Robert J. Person, a partner and banking analyst at Coopers & Lybrand, an accounting firm.
In Massachusetts, the state has taken lifeline banking into its own hands. Earlier this year, the legislature passed a law requiring all state-chartered savings, commercial, and cooperative banks to provide no-fee checking and savings accounts to any person younger than 18 or older than 65.
''The whole issue is a fallout of deregulation,'' Mr. Kneen adds. ''People have taken for granted what were subsidized services.''
''Prior to deregulation, this wasn't a problem,'' noted Kirk Willison, a spokesman for the American Bankers Association (ABA), ''because low-deposit accounts were subsidized with higher-yielding accounts and loans.''
For their part, the banks argue that they can no longer subsidize these services. A recent report by the ABA economics division cited a Federal Reserve study which found that it costs an average bank between $3.75 and $5.32 a month to maintain a transactions account. This was regardless of the size of the account and the number of checks that were written, even if none were.
In the past, banks could cover the costs of these accounts in part from profits earned through low-interest savings accounts and higher-interest loans. But the invention of money-market deposit accounts and Super NOW accounts forced banks to pay higher market rates of interest.
Today, then, banks can either recover these costs through a monthly charge or a charge per transaction. Or they can find more creative ways to get people to leave large balances in an account. This, Kneen says, is one way people can cut or eliminate the costs on transaction accounts. ''If you have a variety of household needs, try to combine these in one account,'' he recommends. For instance, he notes, many married couples have checking accounts for both the husband and wife, as well as a small savings acocunt. If these could all be combined into one NOW account, it might be large enough to meet the minimum-deposit requirements.
Some banks permit customers to count any kind of account toward a minimum-balance requirement, including an individual retirement account (IRA). So even if customers had most of their IRAs in a mutual fund, stocks or other non-bank investment, one could still keep $2,000 of IRA savings in high-yielding CDs.
People who can do without that little stack of canceled checks every month have saved money by letting the banks keep them. Many banks now charge $2 or $3 a month ($24 to $36 a year) extra to return checks. If a copy of a particular check is needed, to prove a bill was paid, for instance, it can be obtained in a matter of days - for a fee, of course.
People who live in urban areas have more choices in banking. If you write many checks each month, call the banks and savings-and-loans in your area. Even if the one with the lowest fees is not near your home, you may only have to drive there once - to open the account. After that, you can mail in all deposits or have your employer deposit your paycheck directly, if that's possible.