Banks, in an attempt to wring more revenue out of customer accounts, are conjuring up new ways to raise fees on basic products like debit cards, cash machines and checking accounts.

As regulation curtailing financial institutions from levying certain charges on consumers has mounted over the past year, banks have had to dream up new fees to replace those now trimmed by laws. Credit-card users have experienced new inactivity fees and foreign-exchange charges, while checking accounts have gotten hit with new monthly maintenance...