This question is meant to serve as a reference for setting up environments in which to test answers that require unusual hardware, processors, etc. Most answers will involve simulators and emulators.
All answers should be Community Wiki, and there should be one answer for each notably distinct combination of obscure factors.
Related questions:
Texas Instruments graphing calculators run a simple OS with a BASIC interpreter on top of a z80 or m68k CPU. Newer calculators, or older calculators running modified software, can also run user-provided binary/assembly code.
An open source emulator for most TI calculators can be found here: https://wabbit.codeplex.com/
For any given calculator, a ROM image will be needed. These can be found at various places on the web.
Launch the emulator, File > Open to load the ROM file, then File > Transfer Files to upload a copy of the BASIC or ASM program from your computer to the calculator.
[please add per-calculator instructions for running a BASIC or ASM program here]
