You have to get a license for xbox, nintendo, etc. before you can buy an SDK from them. They require a statement, and some sample programs, games before they fork over a license.
I'm right now in the process of trying to get a license for Gameboy Advance.
There are plenty of freeware programs that will allow you to program many game systems usually with C/C++ or a hybrid language.
For the GBA for example there is a program called HAM and VisualHam which allows you to program your own GBA games and compile them as roms and test them on an emulator. It uses a Visual C++ type interface and command set.
People who have flashcards (gba) can download your roms and download them onto the card and play them on their gba anywhere.
On other systems like xbox, etc. you will need a modchip to play non-license or many people use this stuff to play copied games.
Modchips can run from 15 to 60 bucks usually. You can buy a pretty sweet Xbox fully pre-modded with an extra big harddrive for like 400 bucks.
check it out here:
http://www.modchipstore.com/product_16167_Brand_NEW_Platinum_Xbox_Customized_Console_w__120_GB_HD.htmlOne good thing about an xbox modchip/system is that you don't need a dvd card installed on it to play dvd's.
Other systems like Xbox, etc. have similar freeware programs availiable as well as communities that support them.