If you are a non-voting shareholder of a company, your rights are limited if the Board of Directors ("Board") subsequently takes action that you do not like. Ultimately, their conduct may be so egregious that you have rights to take action, but generally they are entitled to run the company in ways they see fit. As long as they are not violating the fiduciary duties of loyalty and care that directors owe a company, your hands may be tied.
If the Board is small, and the misbehavior involves only one or two directors, it is more likely that the duties of loyalty and care are being violated. This is simple human nature. If you have 10 people in a room, the likelihood that they are all taking advantage of their position at the expense of shareholders is fairly low. If you have two people in a room, the likelihood that they are both taking advantage of their position at the expense of shareholders is much higher, relatively speaking.
If you have the opportunity to become a shareholder of a small company, it is best to make sure that you are a voting shareholder. This might involve negotiation if the bylaws have not been written. Or it might involve purchasing a different class of stock. If you are becoming a shareholder of a larger company, it may not be in your best interest to have a vote, because there will be an ample number of voting shareholders overseeing the Board.
If you are already a non-voting shareholder of a small company, you are likely entitled to inspect the books and records of the company, depending on the state in which you are located. You generally have to provide notice of a certain duration as defined by state law, so your inspection does not unduly interfere with the company's business affairs.
When a small number of people enter into business relationships, they have competing considerations and different ideas about how a company should be run. In most cases, these disputes are resolved without resorting to the legal process. But even when people are conducting their business in good faith, they might run afoul of the expectations of their colleagues in the company. This could involve compensation or any number of things. In such cases, it is prudent to have a vote on the matter.