As far as I know, the answer is no, but there are some workarounds you can use:
1) If you use Google Chrome, when pasting, you can use Ctrl + Shift + V for plain text
2) If you are using an Office program, Ctrl + Alt + V will do. You can also set the default type of paste inside Office programs by going to File > Options > Advanced > Cut, Copy and Paste and set the default
3) You could use PureText throughout Windows and set up a shortcut key to paste anywhere (default is Windows + V). PureText strips any formatting from your clipboard and pastes it. In fact, PureText is the exact replica of what you are doing currently:
PureText is basically equivalent to opening Notepad, doing a PASTE, followed by a SELECT-ALL, and then a COPY
and the benefit is...
The benefit of PureText is performing all these actions with a single Hot-Key and having the result pasted into the current window automatically.