Can I do money transfers via the Internet with online banking?

In addition to the right answer already posted, PayPal is another option to use for transfering funds online. You can pay anyone with an email address or phone number - instantly! The following info is from their site: https://www.paypal.com/

Founded in 1998, PayPal, an eBay Company, enables any individual or business with an email address to securely, easily and quickly send and receive payments online. PayPal's service builds on the existing financial infrastructure of bank accounts and credit cards and utilizes the world's most advanced proprietary fraud prevention systems to create a safe, global, real-time payment solution.

PayPal has quickly become a global leader in online payment solutions with 100 million account members worldwide. Available in 55 countries and regions around the world, buyers and sellers on eBay, online retailers, online businesses, as well as traditional offline businesses are transacting with PayPal.

Located in San Jose, California, PayPal was acquired by eBay Inc. in October, 2002.
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- Send money to family and friends, forward a gift of money, buy online – PayPal is the secure, free, easy way to pay. Choose from 6 different currencies.
- You control how you pay, too: bank account, credit card or your PayPal balance. From home, work, even your mobile phone. It’s all about choice: yours.
- Pay for goods, services and eBay items
- No matter where your mouse takes you, PayPal lets you shop without sharing your financial information. With PayPal, privacy is built in.
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We Help Protect Your Account — and Your Purchases
PayPal’s industry-leading fraud prevention measures and our one-of-a-kind method of keeping your financial information private from sellers make us a safe way to pay online. Plus, we offer the following to protect your purchases:
- Dispute resolution on PayPal purchases
- Purchase protection on eBay — PayPal Buyer Protection
- 100% protection against unauthorized payments sent from your account.
- PayPal sends an email confirmation of every account transaction.
- If you receive confirmation of a transaction you don’t recognize, our 24/7 customer support team will help you sort out the situation.

The answer is…. it depends on your bank.

Most banks that have online banking resources such as Citibank, chase and Bank of America, allow you to do a variety of money transfers via the internet. You can transfer between accounts, to another person who has an account at the same bank, or even a wire transfer to another bank all together (your account or somebody else's). In fact, banks do not let you do this over the phone, so utilizing the internet becomes much more convenient than schlepping into the bank itself)

Depends on which country yoiur bank is in. many north american banks only allow one to pay a trusted merchant like a electricity company. Offshore banks allow one to send wire transfers internationally online which is nice and thus you could easily pay anyone who is able to receive a wire transfer. For more information on such offshore banks with online wire transfer capability go here:
http://www.panamalaw.org/offshore_bank_account.html