The way I have come to understand it, there is a basic set of signatures, DOS Attacks, etc., that are included, but the fancier application layer stuff is additional, correct?

Not really, there are no basic signature on the ASA itself. ASA has inspection engine for a few protocols but it has different functionality to IPS inspection engine. Here is the ASA inspection if you are interested:

http://www.cisco.com/en/US/docs/security/asa/asa80/command/reference/i2.html

In regards to DOS attacks, there is basic threat detection in ASA, and here is the URL for your reference:

http://www.cisco.com/en/US/docs/security/asa/asa80/command/reference/t.html#wp1482339

Hope that helps.

There are basic IPS signatures in the base ASA code/feature set.

See attached picture of IPS Signatures in my ASDM.

http://www.cisco.com/en/US/docs/security/asa/asa82/configuration/guide/conns_protect.html#wp1056358