Over in the SANS ISC discussion forum, a couple of readers have started a good discussion https://isc.sans.edu/forums/Encryption+at+rest+what+am+I+missing/959 about which threats we actually aim to mitigate if we follow the HIPAA/HITECH (and other) recommendations to encrypt "data at rest" that is stored on a server in a data center. Yes, it helps against outright theft of the physical server, but - like many recent prominent data breaches suggest - it doesn't help all that much if the attacker comes in over the network and has acquired admin privileges, or if the attack exploits a SQL injection vulnerability in a web application.

There are types of encryption (mainly field or file level) that also can help against these eventualities, but they are usually more complicated and expensive, and not often applied. If you are interested in "data at rest" encryption for servers, please join the mentioned discussion in the Forum.