The answer to this frequently answer question is a resounding yes.  Online credit card applications are processed on high security, secure socket layer (SSL) encrypted servers.  However, those who are concerned about online security can take a few extra steps to give them piece of mind.  To verify the security of your personal information, take the following steps:

1.) On any page that asks you to submit personal information, there will be a Padlock which indicates a secure connection. The Padlock will be on the bottom of your browser (the grey part), in the bottom right corner. Double clicking the Padlock will open the website's SSL (Secure Sockets Layer) certificate.

2.) Review the certificate.  The certificate will display the registered owner and verify the security of the connection. For example, if you are applying for an American Express credit card, the verified registrant is www66.americanexpress.com

Do not submit any personally identifiable information, especially your social security number, until you have established that your information is properly encrypted on a secure server. 

Once you have established the security of the application, take the following additional steps to insure your personal information is not left on the computer you are using:

1.)  Make sure your computer does not have any malicious trojans or spyware products.

2.)  Be sure to clear the saved information from forms from your browser.  You can do this by selecting TOOLS from your browser, then INTERNET OPTIONS from the dropdown menu.  Here, you can clear all of your personal information.

The same rules for applying for credit cards should be used for all internet transactions that require you to divulge personal information.  As a rule, it is best not to give any website your Social Security Number unless it is a reliable company with a secure SSL server.