I would guess someone has deleted them. You can add them back in manually using the add new in the top right had corner.
If using PayPal Standard.
Name: PayPal Standard Configuration Template: Payment\PayPalStandard\ConfigurePaymentMethod.ascx user template path: ~\Templates\Payment\PayPalStandard\PaymentModule.ascx class name: NopSolutions.NopCommerce.Payment.Methods.PayPal.PayPalStandardPaymentProcessor, Nop.Payment.PayPal
If the Payment Methods are deactivated (IsActive field in database set to false), then they are invisible in the admin interface. I don't know any other way to activate them, but to set the IsActivefield in the database manually (using SQL Server Management Studio).
Use following SQL query to activate them all:
UPDATE [Nop_PaymentMethod] SET [IsActive] = 1
After that you can deactivate ones you don't need in the admin interface.
@Developers: Will there be a possibility to activate/edit the non active payment methods in the next release?