Depending on your needs, a traditional merchant account or another 3rd party processor like Amazon Payments, Google Checkout, Stripe, 2Checkout, etc. may serve as an alternative.
But there is no equivalent substitute for PayPal. There is no no-monthly-fee, no-credit-check, no-application 3rd party processor that lets you accept all major credit cards, eChecks, bank transfers, and includes all 190 countries and regions PayPal supports, including those where credit cards are uncommon and Google/Amazon/etc do not offer accounts.
In addition, of the fee-free services, Paypal may be the only one that does not require end customers to make accounts to use it. This is, for me, by far the biggest disadvantage to the otherwise competent Google Checkout product.
But there is no equivalent substitute for PayPal. There is no no-monthly-fee, no-credit-check, no-application 3rd party processor that lets you accept all major credit cards, eChecks, bank transfers, and includes all 190 countries and regions PayPal supports, including those where credit cards are uncommon and Google/Amazon/etc do not offer accounts.