Is it possible to queue multiple Steam games for installation in one action?

Since a recent update, you can select multiple games by holding down control and clicking them. Or, if they are adjacent in the list, select the first, hold shift and then select the last.

Then right click the selection, which will allow you to install them all at once:

You should be able to just start installing them as normal, and the Steam client will download them automatically afterwards. Have you checked the Downloads portion of the client? If your downloads are pausing when you choose to install another game, just hit Resume All.

Log into your account at steampowered.com (While connected to your steam client) navigate to your profile: Games -> All games.

You can now "One click" install the games you want to install. Steam will now automatically download and install the selected games.

PS: It will install to default steam install path. So if you have several SteamLibraries, then you are out of luck.

Example: