In classic Outlook for Windows
- Paste as usual with Ctrl+V.
- Press Ctrl to open Paste Options.
- Press T or choose Keep Text Only.
It's also on the Message tab, under the Paste dropdown.
Make classic Outlook always paste without formatting
- Go to File › Options › Mail and click Editor Options.
- Under Advanced, find the Cut, copy, and paste section.
- In Pasting from other programs, choose Keep Text Only.
In new Outlook and Outlook on the web
Paste with Ctrl+Shift+V. If you want the whole message sent as plain text, switch the message format to plain text on the message's Options tab.
If the shortcut doesn't work in your app, paste the text in the box above, click Copy plain text and paste it wherever you want: it will arrive without any formatting.