There are two concerns to local storage in HTML5 -
- One website reading offline data that another website has stored in a users browser
- An end user querying your websites offline data directly
For 1, browsers enforce the same-domain restrictions to localStorage (or the sqllite database support that safari has), so other websites won't have access to the data that you store. However, do remember that if your site has XSS vulnerabilities, it would be possible to steal the data.
For 2, you can't prevent it. Its just like a cookie - the user can chose to view/delete/modify it.
Encryption of data is possible (see http://farfarfar.com/scripts/encrypt/), but pointless. You cannot have a single, global key/password - because an attacker can easily figure the key from javascript code. Using a user-entered password to encrypt/decrypt is possible, but client-side encryption libraries aren't mature or tested well enough. There are likely tons of way to break it.
So, for now atleast, don't store sensitive data in localStorage.