LastPass encrypts your passwords using your master password as (at least part of) the key. This means that they do decryption of passwords client-side as well. The entire password file is not stored locally but they had an intrusion of some sort a number of months back which demonstrated that they have a pretty good system set up along with quite a bit of monitoring. Truecrypt in dropbox is obviously a good choice if you're super paranoid but after seeing LastPass respond to security really well and it having an overall pretty simple UX, I don't have any reason to not recommend it.

The LastPass UX is anything but simple

I use KeePass right now synced with Dropbox - what keeps me up at night is the fact that if the bad guys got my password file today, there could turn out to be a vulnerability in it discovered years from now that could allow them to get my password.

At least you're going to have years to go through your database and change all your passwords.