As I understand it, encrypted transmissions should be reasonably safe, assuming they use https sites and TLS (Transport Layer Security) ;
http://en.wikipedia.org/wiki/Secure_Sockets_Layer You can check which level of SSL/TSL your browser is using. Anything lower than SSL 3.0 is not good, Opera uses SSL 3.0 and TLS 1.0 and 1.1.
What is not clear to me is whether a keylogger on your computer sending the encrypted data to a remote website would enable a cracker to 'unencrypt' it and use it to gain account details. Presumably not, otherwise there would be no point to encrypting the data in the first place!
I remember reading about an exploit about 2 or 3 years ago where some Russian crackers were supposed to have been able to infect the Microsoft servers used by some banks so that they loaded a keylogger on every customers computer, which then sent account details to a specially created website. Steve Gibson's ID Serve tool, which allows you to identify what server software any site is using, will tell you if a site uses Microsoft IIS or Apache/Unix software;
http://www.grc.com/id/IDServe.htm
Not using IE for financial transactions should also improve your security.