This would really take a lot of work...
But, don't worry there's many ways, to do it from the easiest way to the hardest.
There's many tutorials of sprite animating and many programs to make your own!
You can use:
Flash 8 PRO
Flash CS5 i don't remember the lastest version
Flash AE
Synfig
and more...
These are for animation like
The intro of SSF2;
The trailers of SSF2;
And the little cutscenes like - *CHALLENGER APPROACHING!*
But, for making games is more dificult you'll need script skills or script lesson.
Also a little question: what you would make with Flash skills?