May a Board member of a charitable organization be paid?
Yes. Although the vast majority of public charity boards are entirely voluntary, nonprofits are permitted to pay reasonable amounts for services actually rendered. Remember, any payment must be reasonable or you could face an “excess benefits tax.” (See Ready Reference Page: "Charities Must Avoid Excess Benefit Transactions.") Private foundations are more likely to pay their board members, which is also permitted so long as it is not excessive and considered “self-dealing.”
You should also be aware that payment of director fees may disqualify the director from the protection of the federal volunteer protection act or similar protective law of the state.