Hmm, there are many different uses and tones for these verbs, but I think you're asking in the sense of a request.
CAN you open the door?
WOULD you open the door?
In this case, it's simply a matter of formality. My primary school teacher might urge that would is the better question (since strictly speaking, can you do something is just asking if you have the physical ability to do it or not), but both are used interchangeably by native speakers.
So, in short, it's simply a matter of formality. WOULD you do something sounds more polite. Although you can use both, I recommend using WOULD more often than CAN when making requests. It sounds better. :)
For further explanation: