I do exactly that with a Buffalo Linkstation. It's taken until version 3 of the product for the remote access to be even marginally useful, but now it's there.
Remote access is via a web interface. You can set up access permissions locally (e.g. named people or groups accessing certain folders) and have thase permissions reflected on the remote access portion, or you can set them up separately.
You choose a name for your NAS, register it at buffalonas.com, and from then on you can log in to it via bufallonas.com. Once the connection is made, the link is direct. As I said, the user interface in previous versions was hysterically bad but now it's pretty good. You can also manage it remotely, if you discover your in Florida, the box is in the UK, and it's not set up quite right.
I'm sure there are plenty of other devices that can do this, yours may be one of them.
Security is fine: you can force https, so the data itself is secure. Other than that, it's down to choosing strong passwords.
Last edited by Bushfiva; 27th November 2010 at 20:42.