What Database programs/tools are included with OS X?
Sadly, the database tools that ship with OS X Lion are special purpose tools and lack an interface building toolkit. Apple implemented Core Storage for developers and not end users to use and a similar path seems to be likely for iCloud in the next year. The address book is the only card like storage GUI and adapting it for purposes other than storing contacts is painful to say the least.
Let's look over the open source projects included with OS X v10.7.3 that ship and call out the candidate database and key-value store frameworks you could possibly bend to your wishes:
- BerkelyDB
- OpenLDAP
- PostgreSQL
- SQLite
- WebKit
- libsecurity_keychain
I'll leave the various programming languages off the list since that's more of a Stack Overflow answer, but none of these is ready to go with a simple card based graphical user interface. If I had to pick one tool to re-implement hypercard, I would start with WebKit's implementation of HTML 5's client side database storage and use Safari for layout / user interface. This would likely need javascript knowledge as well as HTML / CSS to pull off a workable solution.
In a similar way, you could take tk and one of the programming languages to build up your database and UI logic and hook into your favorite data store listed above. Also, don't overlook iCloud's key-value store since it could arguably be considered "shipping with Lion."
Your constraint of not needing to install additional software is limiting since Apple no longer ships a tool that both stores data and has any sort of usable UI. Even automator can store variables, but you'd be hard pressed to make something of it in practice.
Leaving the run only what is installed constraint opens the gates to many solutions. The best (as of today) card based studying app seems to be Mental Case, but it lacks the database aspect and simple programmability of Hypercard. I haven't seen a single viable hypercard replacement that ships on the App Store, so perhaps some developer will provide exactly the tool needed to fill the gap left by Hypercard.
MySQL used to be installed on Mac OS X by default but it is gone with Lion*. PostgreSQL is now installed standard but it is only available from the command line.
Of course with Xcode you have the ability to use Core Data also, for development - built on sqlite as are many OS X internals.
For users wanting something graphical, buying Bento or something similar is probably the best option. I you choose to work with PostgreSQL then pgAdmin is a good configuration GUI, and free.
Bottom line, if you don't want to install anything else, learn to love PostgreSQL command line.
*since Oracle now own it, licensing has tightened up. I downloaded it to use for a Rails project and very soon after had an email from Oracle asking which license I was thinking of buying... This new ownership is maybe what prompted the change for Apple.