When you work in a large company and run into ethical issues, it really does feel like the only choices are quit or stay quiet. I was in that spot not that long ago and did not want to make a drastic move without understanding what protections actually exist.

While digging around, I found an article in the National Law Review about whistleblower programs that explained how the reporting frameworks work, who qualifies, and what kind of safeguards are in place. Reading through that made it a lot easier to think clearly about my options, because I realized there are formal channels designed for exactly these situations. For me, understanding that those mechanisms existed made it possible to stay put and address the issue in a structured way instead of feeling boxed into an all or nothing decision.
 

I think it makes a big difference whether this is private information you came across in the course of your employment, or public information that you learned of through the news, trade press etc. If the former you should consider informing your manager, HR or compliance department, or regulator, depending on the nature of the problem (you should have received training explaining who the appropriate people to bring different types of issues to are). If it is public events you can discuss them here, and my strong intuition is they do not provide strong reasons for you to resign if you otherwise wouldn't.

I'd say two things:

1. If you are aware of unethical or illegal behavior at the company, I would suggest raising it through internal or external whistleblower channels. For example, you could raise this to your compliance officer or to the firm's attorneys. There are definitely internal channels available to you to report things, even anonymously. Furthermore, there are many external reporting options available to you, some of which might compensate you in the event the company is fined. For example, there are whistleblower programs associated with the SEC, CFTC, FCPA, and AML, which can pay whistleblowers up to 30% of sanctions. If you are considering seeking whistleblower compensation, I would suggest speaking with an attorney first.
2. As far as your specific position at Wells Fargo, I would suggest that it depends on a couple of factors. One is whether your specific role is important to enabling these scandals. For example, if you became aware of LIBOR manipulation, but are working as a bank teller, then I don't think there is any ethics-based reason for you to resign. The other consideration is how the bank would respond to your absence. For example, if the bank were to hire someone to replace you, who would be better at your job, or less likely to raise a whistleblower complaint, or otherwise worsen the scandal, then arguably it would be better for you to stay. Essentially this second consideration asks, what is the counterfactual if you were to resign, and would that be better or worse overall?

Finally, though you asked about ethics, I would also suggest that you consider the effects of your actions on your career. For example, having your name publicly out there as a whistleblower could limit your career options in some ways. On the other hand, you probably don't want to have a position on your resume that is later shown to have been associated with some scandal.