In early May of this year, LastPass announced that it believed that its user database had been compromised, very much like Mt. Gox recently. Here's a link to a story in a respected technical news source, TechWorld:
http://www.techworld.com.au/article/385447/lastpass_hack_fear_leads_password_reset/
I work as a technical writer for a Fortune 1000 firm in the U.S., in a product area that provides security software for use by banks and other institutions that deal with financial and other highly sensitive (usually legally protected) information. I would NEVER use or recommend a cloud-based product to protect passwords to any account that is linked with a bank account that I own or a credit card that I am responsible for. LastPass is a great idea for managing all of those accounts you have to sign up for to get access to news sites or other fun stuff, but not for the accounts that actually matter.
For accounts that matter (your bank accounts, accounts on your credit card site, PayPal, Dwolla, investment firm accounts, accounts with a currency or stock exchange, accounts with your utility company, etc.), you need something local and secure. I recommend keeping those passwords stored in a text file encrypted with GPG or in some other form that uses a strong encryption method. I also recommend backing the encrypted file up on a USB dongle or (even better) a CD that you replace every time you add a password. Finally, use a product that wipes (rather than just deleting) files on the computer that you use to encrypt and decrypt this file, and wipe the swap file every time you access that file. Another option is to use a product that encrypts your hard disk or swap file, or both, such as TrueCrypt or my favorite, Jetico Bestcrypt.
I'm not entirely immune to hackers or a password-stealing trojan; nobody is. But if you do what I suggested, your chances of surviving a hacker or virus intent on stealing valuable information are much improved.