Disclaimer: What I describe below is for a developer. It is not for the public. For example, if you are not a developer and want to get mountain lion, you will have to pay for it.
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You can download full installers for leopard, snow leopard, leopard server and snow leopard server on the downloads page on the mac dev center. But the rest of it is just updates and other stuff.
You can freely get a redemption code for mountain lion on the mac dev center and download it or mavericks 10.9.2 in the mac app store, but you can't freely redeem one for lion anymore. Even developers will have to pay now to get a code for lion. (Free redemption codes were available for this here, but are not anymore).
None of this solves your problem however. And that is how to get 10.9.0. If we want to keep this conversation legal, the answer is you can't legally download it anymore. But you might to get it back from a time machine backup.
I knew this would become a problem when the mac app store was created.
I really appreciate developers offering much older versions of their software on their websites and many developers are doing a better job of this than apple.
Having said that, how to solve the apple problem? Do a comprehensive backup of all full installers!
I have ALL point releases of every full installer of OS X since 10.7 backed up on 2 hard drives and have made bootable usb's of all of them. And whenever I download a new one I disconnect these drives. This is very important because if you don't, one of them may become overwritten by a newer one.
I have sometimes seen on websites advice to overwrite bootable usb installers when new versions become available. I have never followed this advice. If I did, it would have saved me money - but also would have left me stranded when I found out I needed to reinstall an older version!
So now I have a box full of bootable usbs. I have since added to this box bootable usbs of tiger, leopard, snow leopard and snow leopard server.
I have another box full of bootable dvds and cds.
This stuff is messy, but a necessary mess if you want to keep it legal.
It's something you may hopefully never need, but when you do, you are very glad you kept all that mess.
Since apple do not have a comprehensive archive of their older systems available for download, to do it legally you need the boxes of mess - or hard drives full of stuff you will probably never need.
If you haven't yet made such backups manually, you might be able to extract some or all of them from your time machine backups, depending on how far back they go.
If you can only find the .0 versions in time machine backups, (i.e., 10.7.0, 10.8.0 and 10.9.0) that would still be OK because you could then use the updates on apple's website to update to any other desired point release.
This of course assumes time machine backed up the full installers when you first downloaded them, which sadly is not necessarily so. That is something you will have to find yourself.
It also assumes you got these as soon as they were released.