I've heard great things about mint.com - it comes highly recommended from such trusted publications as Kiplinger and Money magazine.

Mint claims that they don't store your banking passwords or other credentials and that they only connect you directly to your financial institution which should make transactions as secure as they would be directly with the institution. They don't keep credit card numbers or bank account numbers.

Also, according to Mint, they use 128-bit SSL encryption for security. The site has received the VeriSign security seal and is tested daily by Hackersafe. The privacy protection standards are certified by TRUSTe. Depending on your level of confidence in those companies, that may be reassuring. You can read their FAQ for information directly from the site: http://www.mint.com/privacy/faq/

That said, I've had no personal experience with it. Sorry that I can't give you a better answer. Perhaps there are other readers out there who can chime in?