How Secure Are Online Password Managers, Anyway?

Online password managers, such as Lastpass, are a great convenience; they allow easy secure access to your passwords, and allow you to use more complex ones, as you don't need to remember each individual password - just the master password that secures your password manager. However, in light of recent NSA revelations - how secure are those things, really? PCWorld has the scoop:

The NSA is decrypting all things. You might have your passwords stored with a password management tool, such as the popular LastPass or 1Password apps. Should you be worried? Yes and no.

This question was posed on Quora: Is it reasonable to assume that developers of popular password management software are/will be forced by law enforcement to install backdoors in their encryption algorithms?