TI certainly have certainly seen off rivals such as HP or Casio to capture the lion’s share of the calculator market. The TI-84 is a real staple, and with as many units as there are out there, hacking them is a given. However, selecting an operating system for the machine can be a hassle. TI-OS is proprietary and doesn’t really want to let you do everything you’d like to. There are alternatives, but many of them won’t let you easily use your calculator to be — well — a calculator.
[Siraben] has zkeme80 which is essentially ANS Forth (mostly) with extensions for the TI hardware. You can easily extend the system, of course, because it is Forth. You can also use the machine for its intended purpose easily.
Underneath the Forth system is a Z80 assembler and Scheme, if you want to do some heavy duty changes. The OS borrows from an earlier Z80 Forth which started out with the venerable JonesForth. It also leverages low-level code from SmileyOS which, in turn, uses code from KnightOS.
If you want to experiment with the system and you don’t have a TI-84+ handy, maybe you can find one in your browser.