Is it possible to list all of the Steam games I have downloaded?

In the Steam client:

1) Click your username from the top right, then click 'Account Details', to go to your Steam store control page.

2) From the Steam store control page, under the 'Store & Purchase History' header, click 'View licenses and product key activations'.

This page shows, in chronological order, what games you have acquired and how (Steam store, retail code, complimentary copy, or gift). Unlike the other methods above, this activation history includes any free games you may have previously installed, but deleted.

By simply installing Steam and going to the Library, there should be a list with all the games you own.

If there isn't, still on the Library page there's a search function in the upper left part of the screen. From there, you can access a drop down menu where you can choose what to list.

If you choose "All Games", you should see all the games you own on Steam and can redownload and reinstall whatever you want.

There is an additional way to view Steam games you own.

After logging in to Steam you can view your account's licenses by vising this webpage: https://store.steampowered.com/account/licenses/