My church has a specific time during the service where people can go off to the sides to put there money in a box or basket. People can give cash, checks or fill out an envelope if they want their offering to come straight from the bank. They can also give electronically.
Since the beginning of our church, our pastor's wife has collected the offering an done the books, and then sent out charitable giving letters at the end of the year for tax purposes. I've almost always filed for the tax deductions because I want the government to keep as little of the money I've earned as possible.