I had no idea about this, but here is the warning directly from Chrome. When you login into any computer, Chrome will download all your sync information and store it on that computer.  Even when you log out!  You have to actually DELETE the account to get rid of this information.

Direct quote from the Google Chrome site:

Don’t sign in to Chrome if you’re using a public or untrusted computer. When you set up Chrome with your Google Account, a copy of your data is stored on the computer you’re using and can be accessed by other people using the same computer. To remove your data, delete the user you are signed in as.

So there you go kiddies, surf safe!