I try to style my games after old crude amateur indie games and flash games, cause thats kinda what my games really are, crude indie games made for mine, my friends' and sometimes other peoples amusement (cause sadly i havent gotten much success yet, but maybe someday!)
For me atleast the trick to achieving the effect is first having played alot of those games, simple movements and animations, primarily flat colors with simple shading, exaggerated features and that kinda jazz