Use two-factor

The main defence against simple keyloggers is a second factor - if the authentication process calls your phone (like Google Authenticator or Duo Security), you will know some hacker has got your passwords and is trying them out. Since most keyloggers are installed en masse, this is quite a useful defence.

LastPass is a good password manager (free as in beer for desktop OSs, paid-for on mobiles) which now includes Google Authenticator support and has some other two-factor options (grids, biometrics, and Yubikey). See http://lastpass.com/

Although LastPass has the weakness of a cloud-based point of attack, the two-factor options make it more secure against keyloggers than the password managers listed here. It's still vulnerable to a targetted attack against the LastPass client plugin, but that's true of almost any authentication technique.