The ability to install various hacks and modifications of course.
What are the hacks people find most useful -- that is a slightly different question. I will list my favorites:
- screensavers hack -- custom screensavers on non-Special Offers Kindles. Can be your own specified images, an image of the last thing on the screen, or (my favorite) the cover of the book you are currently reading.
- skipstone -- alternative browser, much better than the default one (it has tabs and bookmarks and stuff).
- Collections Manager/librariansync -- manage collections much easier than the default UI, even sync collections with calibre for efficient metadata filter rules.
- kterm -- command-line access to the Kindle, comes in useful sometimes.

- Rescue Pack & Cowards Rescue Pack addon -- if your Kindle ever gets bricked, having these installed might just save an otherwise worthless device.