I would like to be able to store my ever growing collection of downloaded games for easy retrieval instead of taking hours and hours to redownload.
I think games from most companies allow you to save the installation files you download -- or at least the bulk of the files. But the best way to archive your games is going to depend on where you got them and whether you intend to play them on more than one computer.
With games from GOG and DotEMU, just save the installation files that you download.
With The Adventure Shop, save the files that you download. I think your computer remembers the activation even if you uninstall the game (unless you reinstall Windows or get a new hard drive). Games bought from Frogwares would work the same way. Activation information is stored separately from the game folder.
Gamersgate allows you to save most of the files needed for installation -- except for a small setup file that usually needs to be re-downloaded at the time of installation.
With Big Fish casual games, you can save the folder of the installed game. But if you want to play on a computer other than the one you originally installed on, you may end up having to re-download to get the games activated.
If a game requires the use of the registry, and makes registry changes during install, you need to go through the install procedure rather than just copying the game folder.
If you install games on an external drive, and then attach that drive to another computer where the games have not been installed before, it isn't predictable whether they'll all work. The Big Fish games will probably work as demos, then expire. Other games may need the registry changes that would have been made during the install -- and may not work at all, or may have bugs.