Giving up personal info to a third party? No way. That includes programs, services, clouds, using third party computers or networks, or wherever, as long as it leaves your personal computer. You're going to be OK 99+% of the time. Its the other 1% that spells disaster. 1775 has the right idea, don't give it to anybody except the website you're wanting to access with that password. Even then, change passwords often on sensitive information (online banking, credit cards, etc). I've seen people doing their online banking using the public network at a restaurant, just last Thursday at a local Schlotzky's (sp?) restaurant.
I'd use a 3rd party app to store so-called "annoyance passwords" for non-critical websites that force you to create an account using non-personal data, where it doesn't matter to me if they get published in the New York Times front page the next day. But that's about all.