The banking industry is not like most other industries, where there are a large number of small, medium and large businesses providing the same service to different customers. Rather, there are only a few banks, and most of them are reasonably large. One term paper topic could be to examine this facet of the banking system: why is it consolidated? Is consolidation a good thing? What problems has consolidation caused?
The money system depends upon the Federal Reserve to function, as this is the arm of the government in charge of increasing or decreasing the money supply. There are many term paper topics available about the Fed, ranging from how much it actually affects the economy, to why it exists, to an exploration of some of its key criticisms. There is a wealth of information on this issue, with many people supporting and many people decrying the Fed's existence, so there will be plenty of available research material.
The Federal Reserve has a chairman, and the person who fills that role wields a lot of political and economic power. You could examine whether this statement is true by comparing various leaders. Alan Greenspan, for example, was the chairman of the Fed for a long time. How was his performance? Could he have done better? Has his successor done a better or worse job, or is the chairman ultimately irrelevant? These questions can all be explored and partially answered in a term paper.
Banks don't just keep your money in an account for you. They make a substantial portion of their income by lending the money you and other customers deposit to other people and businesses. You could examine various lending trends and policies and make some judgments on the banking system based on these. Was the lending prior to the 2008 financial crisis predatory? Should predatory lending be allowed? If so, what constitutes predatory lending? These are all interesting topics that have a lot of information available for you to research.