With the shortcut or the menu
Press Ctrl+Shift+V (or ⌘ Cmd+⇧ Shift+V on Mac) to paste the text with your document's style. If you prefer the mouse, go to Edit › Paste without formatting.
If you already pasted formatted text
Select the text and press Ctrl+\ (⌘ Cmd+\ on Mac), or go to Format › Clear formatting.
When copying from Google Docs to somewhere else
When you copy text from a document and paste it into a form, a CMS or an email, the Google Docs formatting comes along with it. Use Ctrl+Shift+V at the destination if it's a website.
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.