Right now lastpass encrypts in the browser and the company only saves a binary blob that they can't access. So your data is safe. But they said, "As we become part of the LogMeIn family over the next several months, we’ll be releasing updates to LastPass, introducing new features.." that makes me nervous.
The comments here have lots of suggestions like keepass, but none of them really compare with the Lasspass Android support where it will automatically log you into apps.