I spend a significant amount of my timing deal with ecommerce and different shopping systems. One of my all time favourite solutions is using PayPal and Magento together because they have been designed from the ground up to interact well together.

International Acceptance
PayPal is accepted in many countries and is capable of doing automatic currency conversion.

Integration
PayPal is very easily integrated in all open source shopping carts, and is often freely available requiring very little work for developers.

No Monthly Fees
Many of the other merchant systems require monthly payments even when your business is closed. PayPal charges a per transaction fee which all of the merchants also charge! If you’re accepting debit the transaction fee could be fairly expensive, but usually it is much cheaper for credit card transactions.

Lots of Payment Options
PayPal does e-checks, American Express, Visa, MasterCard, and Discover. PayPal is expected to release applications for smartphones, and the iPad very soon which will allow you to use your device as a wireless terminal.

Secure
You won’t need to spend time worrying about PCI compliance, because the credit card transaction is actually stored and processed on PayPal’s end. Money is usually transferred immediately for credit card transactions.

There are some other shopping solutions available, but don’t expect them to work as well or be as affordable PayPal.

Hope this helps!