That's what strikes me about any system that stores all of your private data - if somebody manages to hack that system then you have lost everything in one hit!
They'd have to still have (or guess) my password, as it's all encrypted on the site. If not, they'd be stuck with brute force attack which would take roughly a year of super computer time, so I would have time to change all my passwords before that.
I have literally hundreds of accounts (oh, turns out it's 550!?), all with a different email addresses, so keeping paper record would be unwieldy. Using a service protects me from phishing (it won't offer to fill in the password if the URL isn't correct). They are also proactive in reporting any security issues with any sites I have accounts with to alert me to change the password, as well as alerting if they notice any suspicious activity on their servers. They provide an onscreen keyboard if I am somewhere (like an internet cafe) where I might be worried about keystroke loggers.
I did seriously think about it before committing to it, but decided it was overall safer to use such a service than not. The biggest risk is me becoming careless with that one password, so I keep that close to my chest.
What no one should ever do is use the same password at multiple sites. Hackers who get a list of passwords and email addresses will immediately try them on every site they might be able to steal money from (eg
ebay and paypal).