Is there a way I can programmatically download the latest version of Craft? If you have a base install script that you use to quickly turn out a new base install for Craft, it would be very useful for that script to be able to download the latest version of Craft when doing it’s new site setup logic.

What’s the best way to do that?
In Craft 3:

You can download the latest Craft 3 release in zip or .tar.gz format by going to:

https://craftcms.com/latest.zip
https://craftcms.com/latest.tar.gz


Or since Craft 3 is Composer based, you can modify your composer.json's craftcms/cms line to install the specific version you're looking for.

In Craft 2: 

You can get the latest Craft 2 version in either zip or tar.gz format by going to:

https://craftcms.com/latest-v2.zip
https://craftcms.com/latest-v2.tar.gz