Looking for a program that re-downloads setups

Chocolatey + Boxstarter

Chocolatey is a package manager for Windows. It is essentially a database of install scripts (from moderated user contributions), which download and run the setups for you.

For example, the command choco install vlc will download and execute the install script for VLC, which in turn downloads VLC's installer and runs it silently (no user interaction required).

Boxstarter is a program which can install a list of Chocolatey packages and set various Windows options (e.g. visibility of hidden files in Explorer).

Installing proprietary software requiring license keys is - generally speaking - possible. However, it depends on the targeted software, e.g. Microsoft Office 2013 allows for silent installations configuration files including license keys. In addition, you would need to find a Chocolatey package for it or create one yourself.

Ninite

Ninite is another package manager. The packages are solely contributed by the company behind Ninite contrary to Chocolatey user-contributed (but moderated) packages.

I quite like the comparisons which are made on Chocolatey's GitHub wiki page. Here is the final conclusion:

Ninite is a solid solution if you don't mind not being able to script it and only install the applications that it has listed on the Ninite page. You are, however, guaranteed that you have everything you need to install sheerly by having the Ninite Installer. In that way it is better than Chocolatey, which most packages require access to the internet to download installers that do not have distribution rights with them (Ninite does not incur this extra point of failure).

Chocolatey has 600% more packages than Ninite and a community that is driving to continually make it better. If you need to get to older versions of packages, many of the packages on Chocolatey.org allow for this. What chocolatey lacks in the guarantee that Ninite provides, it makes up for in features and options. Chocolatey can provide packages for non-free products, have multiple sources and folks can script the installations. Chocolatey is more than just an installer and with that does not require administrative privileges to use.

Both solutions suffer from the issue of having the most up-to-date packages available, it's just that Chocolatey is more transparent about it.

Whether you use Chocolatey or Ninite, consider that the two answer the same question differently and that is okay. They can live in harmony with each other and at some point Chocolatey may offer Ninite as package source.

(Source: https://github.com/chocolatey/choco/wiki/ChocolateyVsNinite, license: probably the same as the code: Apache License 2.0, authors: see here)