Couriers all set their own policies as to what payment methods they're going to accept, just like companies in any line of business. There are some payment methods which are accepted almost universally though, and some which are less common. For instance, the one payment method that you can count on almost any Arkansas freight service to accept is a company check if you're an account holder with their company.
On the other hand, the acceptance of other method of payment can different a great deal from company to company. Almost no couriers will accept cash unless you're paying at a depot for a dropped off shipment in advance. Very few accept online bank payments or PayPal although both of those methods are growing in popularity. Likely the second most widely accepted form of payment for your order is going to be credit cards.
Many people like to pay for their company's shipping needs with a credit card because it consolidates all of their expenditures in one easy to reference statement. While your courier should accept your credit card, you should always verify that beforehand, as there remain several couriers which do not.
Be sure to ask your courier what their credit card policy is. They may have different policies for account holders and for people who pay for each shipment in advance. For account holders, they may simply prefer to keep your credit card on file and automatically bill you for your shipments each month, something which can be very convenient. If you are paying for each shipment, the couriers may have portable credit card units which they can bring to your location, or they may require you to pay with a credit card online or over the phone prior to courier dispatch.
The final bit of advice for those who want to pay their couriers via credit card is to make sure and ask your courier if they accept your particular credit card before you try to pay your bill with it. It is not as complicated as it once was, with many of the more obscure credit cards having faded away, and with most companies now accepting all major credit cards if they accept one, but it never hurts to double check. Failing to do so can result in a very embarrassing situation if you try to pay and realize that your payment method isn't going to be accepted.