You can paste into a plain text window to get what you're after. In TextEdit, you can switch your window to plain text with Format->Make Plain Text (Shift-Command-T).
You could also always paste into something which
only understands plain text, like Terminal. Hmm… Come to think of it, speaking of Terminal… You can also use this Terminal command to convert the current pasteboard to plain text:
After running that, you can paste into a rich text target without getting rich text from the pasteboard. For more convenient access you could put that into a shell script and place it on your dock (or make an Automator script or AppleScript to run those commands) or something.
(But I typically use a plain text TextEdit window to accomplish the same end.)