I pretty much agree with Remus Rusanu's answer.
Maintaining good security is hard, but you can always pay attention to what you do. When ever you access sensitive information carefully verify your query and make sure it cannot be spoofed or exploited to gain access to information which shouldn't be accessible by given client.
If you can roll out physical access to the box by the attacker then there are several things you can do to harden your security. First of all I'd configure ssh access only to only allow connections from specific IP or IP range (and of course no root access). You can also do that that on your firewall. This would mean that the weakest link is your server (the application which receives data/requests from clients, could be web-server and whatever scripts you use). Now you "just" have to make sure that no one can exploit your server. There are a lot more things you could do to harden your system, but it think it would be more appropriate to ask on ServerFault.
If you're worried about physical access to the PC, there isn't really much you can do and most stuff has already been mentioned in Remus answer.
There's also another option. This is by far the most ineffective method from speed and ease to develop viewpoint, but it would partly protect you from any kind of an attack on your server (including physical). It's actually quite simple, but a bit hard to implement - only store the encrypted data in the database and handle all encryption/decryption client-side using javascript or flash. Only the client will have the key and data will always be transfered over the wire and stored in encrypted format. The biggest drawback is that once client forgets the key there's no way back, the data is inaccessible.
Of course it's all matter of time, money and effort - with enough of these anything can be broken.