OS X and iOS have this, it's called Keychain, and it even works cross-device[0] totally securely[1]. Safari recently (I can't remember when) started suggesting passwords, too. Being built into the OS makes it an order of magnitude more likely to be used than a third party application, in my opinion.

[0] http://support.apple.com/kb/ht5813

[1] i.e. Apple (claims it) can't access your passwords, despite syncing them across devices.