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In versions of Outlook pre-2016, this functionality existed in the Move To: Quick Step. It was renamed Archive in Outlook 2016, and there's a larger button, but it's the same as the old Quick Step.
In Outlook 2016, if you hover over the Archive button, it tells you that Backspace is also a keyboard shortcut. I can't speak for other versions of Outlook.
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Archive in the ribbon archives an entire folder.
To set up hotkey archive of individual or groups of emails, right-click an email in your inbox, go to Quick Steps > Create New. Then you can set up a quick step and select a hotkey combination.
Oh, I was unfamiliar with Quick Steps. As it happens, "Move To" has been renamed to "Archive", and indeed you can assign it a keyboard shortcut. Alas, the keyboard shortcuts are limited to Ctrl+Shift+Num, which is a bummer, as Ctrl+Shift is awkward on Kinesis keyboards... – rianjs – 2016-06-28T14:46:57.683
I edited your answer to include step-by-step instructions for assigning the keyboard shortcuts, and to explain a bit of the UI changes between Outlook versions. (Just in case my comment above looks ridiculous to someone else with the same question. :) ) – rianjs – 2016-06-28T17:02:15.530
2Cautionary note: if you're on Outlook 2016 for Mac and using a PC keyboard, the backspace key does not Archive the message - it deletes it. The correct shortcut on Mac is CTRL+E. – D Coetzee – 2017-06-14T18:09:07.203
2Another cautionary note: in Outlook 2013 for PC the backspace key also does not Archive the message, but deletes it. – Paul – 2018-02-14T23:26:40.303