When people ask you for favors is it better to explain to them why you can not do it?

Immature people tend to get offended when you don't give them a reason. A matured person would just say okay thank you and walk away.  But it depends on the situation. 

Think.  Has anyone EVER GIVEN YOU A GOOD REASON why they can't do it?   Then do the same and use the same words.

It would certainly depend on what the favor was, how inconvenient it would be, and why they needed help doing it.  If it was within reason and I could do it without being late for work or something like that then you should try to help if someone asks.  However, if you are being taken advantage of and you end up enabling a person to depend on you then you have a problem.

It would be polite to give a reason why, not that you just don't want to. 

It's fine to say you can't do it now. 

No explanation is needed, if they ask for one, just tell them i just cannot do it. Never tell them the reason.

If you have a genuine reason why not, just explain

I don't give explanations or excuses for saying "no".  No means now and that's how it is.  We owe no one reasons for our actions. 

You have to be nice but firm and saying that you can't do that. You can explain yourself but you don't have to

It depends on who's asking, what the favor is.