I would like to play Super Mario 63 on my work laptop, but not in a browser. I have only found the game embedded on a site. How can I download it?
To generalize: there are flash games you are allowed to download and distribute and there are flash games which are not allowed to download and distribute,
Companies that allow you to make a login and download flash games to play them locally and/or copy them to your own site (i have downloaded about 45.000 flash games) among others:
If you want to have a lot of options around this like auto downloading etc..., then install XAMP, WordPress and http://wordpress.org/extend/plugins/myarcadeblog/ and you can run this semi automatically in other words: it acts as a GUI for all of this. Notice that XAMP installs a local webserver that enables you to play the games on your localhost.
It is not possible to run flash games without installing flash.
Super Mario 63 can be downloaded as a standalone executable (not sure if it need Flash) from Runouw's (the creator's) site. However, the site seems to be low on bandwidth right now, so I can't give exact instructions.
You need to have the Flash Player Projector for your platform. Depending on the installer, there might not be a way to get around installing, especially on Windows. Mac OS X installer packages can be manually extracted, so no big deal there. Windows installers are trickier and often do registry updates (the big deal breaker).
If the machine in question is a Windows machine, try installing the Flash Projector on a Windows computer you admin and then copy the Projector application to the other computer and see if that works.