Unfortunately, you cannot. Amazon's ebooks are all formatted in either AZW or TPZ. With TPZ I don't think is at all possible to convert, it's chained to Kindle. AZW in theory might be possible to convert, but you'd have to remove the DRM encryption, which is illegal. That would strip it down to basically MOBI, which could then be converted to EPUB.
This is one reason I hate Kindle, it's very monopolistic.
Just out of the challenge and curiosity, I wonder if it's possible to load the Kindle version of an eBook in the Kindle PC reader app, then do that thing that you mentioned in another post, with the PDF printer, and just save it as a PDF.
| "Wisdom cannot be given unless someone asks for it and shows a readiness to receive it." |
I would venture to say that the PC reader app does not support a printing option. Maybe someone who uses it could shed some light.
I would venture to say that the PC reader app does not support a printing option. Maybe someone who uses it could shed some light.
Good call, it doesn't have a print function built in to it. I tried a couple of quick little tricks to see if I could make it print anyway but no go. If I find time I might have to roll up my sleeves on this one ... you know ... for the "challenge". 
| "Wisdom cannot be given unless someone asks for it and shows a readiness to receive it." |
If you really need it, and plan on doing something that's toeing the legality line, why not just remove the DRM encryption? I'm sure that would save you time.
I would never toe the line of legality
(I also never go over the speed limit (unless I'm jogging)) 
But just out of curiosity sake, since the DRM removing stuff seems to already be "out there" I guess it just boils down to the OP's original question; How to actually get your hands on the ebook file itself. When I downloaded a free ebook to the PC Reader, I was able to find the file locally on my harddrive, but when trying to open it back up in the PC reader on a separate computer (my laptop) it errored out. Said bad file or something, can't really remember. I only played with it for about 5 mins though, so I guess it's something to keep trying.
| "Wisdom cannot be given unless someone asks for it and shows a readiness to receive it." |
You'd need to use MobiDEdrm. In the past this would also require you to install Python, since MobiDEdrm is all Python scripts. I honestly have no knowledge of whether or not this is still the case.
In the past, you would also need to know someone that owned a Kindle in order to get the PID. Once again, things have changed, and there is now the PC App, which I assume has alleviated any need for that step.
I'm sure Google could assist more, since, once again, I'll state that the above process is neither encouraged, nor allowed by our loving government.
I want tocan say yes you can convert them ! Note may not be worth it but it's Possible !
First off if you buy something on Kindle it Copyrighted to Kindle
so converting it to work on Nook is sorta illegal or gray market area the reason I'm not going to say how to convert it , but say you had a jailbroken iPhone and bought the books on Kindle
on it and also wanted to read them on your Nook you can carefully transfer them and convert the format to MOBI !
Well if you want to resaerch it for yourself their are Hints in this post how to do it yourself but I'm not responsible for any doings of it !
Side Note: If you still have a Kindle copy on a iPhone or other device, some say its not illegal but thats a decision you need to make not Me ! ( Once again Neither GeekDrop or I is responsible for any info in this post )
-- Jayson Krause

Olympus
Single & Not Looking
I don't own a Kindle
and have never used one so if anyone else knows hopefully they'll post. I believe as long as you can download the actual ebook file itself (I think they're either a .lit or .mobi file) then you'll be able to convert it to a file the Nook is able to read, (like .epub or .PDF) using a program like Calibre.
I've also never purchased an eBook from Amazon so I'm not really sure how that all works; whether it goes straight to your Kindle
or if you can just download the eBook file itself.
Somebody please correct me if I'm wrong.