Lastpass appears to be a good way to keep a running list of passwords but is it secure?

After spending the last few days battling someone who learned of my password sequences, it seemed like a good time to figure out a better way of handling passwords. Generally the same password is not used on different sites. This was not always the case and I had some legacy sites in which I did not modify the passwords. This was a big mistake. Never use the same password on two different sites.

I keep a notebook with the site name, user ID, and password. Sadly, I can end up somewhere and do not want to take out the notebook or I have left the notebook somewhere else.

What do you use to keep your passwords safe? Do you use Lastpass?