Paste and Match Style is ⌥⇧⌘V
Apple’s list of Mac keyboard shortcuts calls ⌥⇧⌘V Paste and Match Style, and describes it as applying “the style of the surrounding content to the item pasted within that content”. In Apple’s own apps, such as Mail, Notes, Pages and TextEdit, the same command is in the Edit menu, which is the place to look when the keys slip your mind.
Strictly, it is not plain text. The pasted words take on the font and colour of the paragraph they land in, which in an email or a document is usually what you wanted. In an app without the command, the keys do nothing.
Google Docs uses ⌘⇧V
In Google Docs the command is called Paste without formatting, and Google lists its shortcut as ⌘ + Shift + V. It is also in the Edit menu that Docs shows inside the page.
Where SSPaste gets in the way
SSPaste opens with ⇧⌘V, the same keys. I picked them as its default, and this is what it costs: when an app registers a shortcut with the system, the keys go to that app and the one in front never sees them. With SSPaste running, ⇧⌘V in Google Docs opens SSPaste instead of pasting without formatting.
There are three ways round it. Docs’ own menu still works: Edit › Paste without formatting. SSPaste can do the job itself: with its list open, select the item and press ⇧Return, and it goes in as plain text. Or record different keys in SSPaste’s Settings › Shortcuts, and ⇧⌘V belongs to Docs again.
Plain text from your clipboard history
In SSPaste, plain text is one key away. ⇧Return pastes the selected item as plain text, in the tray and in the list beside the pointer. In that list a ⇧-click does the same, and so do ⇧⌘1 to ⇧⌘6. Select several text cards in the tray and ⇧Return joins them into one piece of plain text, one item per line.
If you never want formatting, Settings › General has Always Paste as Plain Text. Every paste is then plain, and so is every card you drag out into another app. Pasting straight into the app you were using needs a permission from macOS, and why SSPaste asks for it has a page of its own. Without it, SSPaste copies the item and you press ⌘V.
Taking the formatting out of a whole document
If the formatting has already come in with the text, open it in TextEdit and choose Format › Make Plain Text. Every style in the document goes, and Apple notes that the document is then saved as a .txt file. Copy the text back out and it is clean.