Aside from Unity, which of the many desktop environments support switching among the currently open windows using Super+1/2/3/…/9?
Reasoning
This is especially handy if you often switch among the same few apps, e.g. a browser, a file manager and an editor, but also have other apps open, so Alt+Tabbing to the desired window would take more time.1
That keyboard shortcut saves me probably 5 seconds per minute on the average, so ~40 minutes a day, and it's supported by Windows 7 as well. Adding custom keyboard shortcuts for the app doesn't work, because pressing the shortcut will launch a new instance of the app.2
1. The DE will order the most frequently used windows first, but you have to first look and see how many times you have to press Alt+Tab; while with Super+1 or Super+2, you always know which shortcut goes to one app or the other.
2. Some apps have an option to allow only one instance, but this is the exception rather than the rule, and even in that case, there will be a noticeable flicker of launching the new instance and seeing it exiting immediately.
Best Answer
Desktop environments supporting Super+number
These support task switching via Super+number out of the box, and require (almost) no configuration.
KDE Plasma
This was implemented in Plasma 5.9. You still need to uncheck "Keep launchers separate" in the Task Manager Settings to preserve the 1..9 order, otherwise the numbers will be reassigned as you close/open the applications.
GNOME 3 (Ubuntu 20)
GNOME implemented Super+N app switching in Jan 2019. Here's a screenshot of GNOME 3 in Ubuntu 20:
Ubuntu 18 GNOME
Ubuntu's tweaked version of GNOME supports Super+number, with one annoyance: when switching to an application with more than one window (often the case with Chrome/Firefox), you have to further choose which of the windows to switch to.
Unity (Ubuntu 16)
Supports the key combo by default. If the app is running, Unity will switch to it. If it isn't, it will be launched.
Linux Mint Cinnamon
As of version 20, Cinnamon supports Super+number for the "Modern" panel layout.
The feature isn't very discoverable because Cinnamon doesn't show any number tooltips over the taskbar icons when you press Super.
Note that the feature was tricky enough to take years to implement after it was first requested in 2015, then by myself in 2016.
DEs with support via extensions/plugins/applets
Note that letting plugin authors build such a feature is fraught with problems. In several years, I haven't found any plugin/extension/macro/whatever that gets this right. This sort of feature needs to be well-integrated into the window manager, and this was confirmed by one of the authors of MATE Desktop, who agreed with me.
DEs that don't support Super+number out of the box