Degrees of politeness and formality

There are a number of ways of making requests more polite or formal in English:

- Use past tense verb forms.
Can you shut the door, please? - Could you shut the door, please?
Will you tidy your room, please? - Would you tidy your room, please?

- Use introductory phrases. This changes the word order in the request.
I'd be very grateful if you turn the radio off.
Is it allright if I close the window?
You can also use introductory phrases to apologise or explain something.
I'm sorry but Mrs Smith's not here today.
I apologise for arriving so late.

In the most polite and most formal requests you use the past tense forms and introductory phrases. but if you are too polite or formal with your friends they may think you are being unfriendly or insincere.
I was wondering if you would do me a favour, please.