To explain further, the differences between the three types of analog cables are basically:
Composite: Simply dumps the entire signal on to one wire.
S-Video: Separates chroma and luma signals for a sharper picture.
Component: Separates the signal into its "component" colors (red, green, blue), each with unique chroma/luma settings. With the way EDTV/HDTV signals work, component is the only connection outside of a digital one that can transmit downconverted digital signals in a way that your EDTV or HDTV can understand. That means that, despite it being an analog signal, a component connection can be used to "instruct" your TV to display in progressive scan (480p), 16:9 widescreen, or - in the case of the Xbox 360 - 720p or 1080p.
Component isn't quite as good as HDMI at transmitting those instructions, though, because, as an analog signal, it's still susceptible to signal degradation and inexact transmissions. That's why MS decided to support HDMI in their newest iterations of the 360.
VGA is kind of a weird case, because it wasn't designed for use with anything other than a home computer. I wouldn't buy a VGA adapter for most systems, because what it actually is is a little box that converts the outputted signal to something that can be displayed through a VGA connection. In other words, it's trying to mold a square peg into a round hole, and the result is predictably awful. Signals from VGA converters usually suffer from washed-out colors and other such problems.
The sole exception is the Dreamcast, which actually includes support for VGA converters in its hardware. But even then, not all games display properly.
"'Casual games' are something the 'Game Industry' invented to explain away the Wii success instead of actually listening or looking at what Nintendo did. There is no 'casual strategy' from Nintendo. 'Accessible strategy', yes, but ‘casual gamers’ is just the 'Game Industry''s polite way of saying what they feel: 'retarded gamers'."
-Sean Malstrom
