Personally, I wouldn't put stuff up on dropbox without securing it first. Dropbox doesn't use a "zero knowledge" encryption policy, they simply encrypt locally, control access and 'prohibit' employees from looking at people files - and monitor it. That doesn't make me comfortable at all.

I use various combinations of either local machine encryption, Truecrypt or Boxcryptor to encrypt the dropbox folder LOCALLY (with zero knowledge of the keys to the provider OR dropbox) and then it syncs automatically up to dropbox but it resides there ENCRYPTED so that even if they get to the file it can't be read by them at all.

This makes it nearly impossible to share files with others directly from your dropbox, but that's not what I use it for anyway.

Boxcryptor is pretty simple to use and implement and they even have mobile apps so you can continue to use it on a mobile or ipad/tablet. It's pretty much free. I've used the free version for several years.

edit: But, now that I RE-READ your post, i guess you want browser access too. Don't think my solution would do that for you, although I know there is a way to use the key on another local machine with authentication.