Its better to use a Flash microcontroller.

If you need to change the firmware or download it many times, as Erik suggested you'll need to add circuitry to run the program in external RAM.

If you are looking to scramble up your code to make it hard to crack or reverse engineer, you could do a hard technique of loading EEProm with stack images for certain tasks and use it as the thread to tie the internal routines together.

Runtime process:
Copy EEProm block to stack ram area.
RET

The prepackaged stack values string the process together, each routine ending in RET. The last RET pulls up a vector to the task matrix manager.

This allows you to also put all sorts of garbage in between real routines to confuse disassemblers. Desync blocks and similar but meaningless routines can make it very complex the re-thread. :)

Its an interesting process but not for the unmotivated.

aka J --- been there done that