You can create a simple 'service' using Automator, which you can then use to copy items with. It won't work for copying in apps that don't support Services (Office, cough), but for copying stuff from Safari etc. it's fine.
- Open Automator
- Pick 'Service' from the suggested templates
- Make sure the top line of text and pulldown menus on the right reads 'Service receives selected text in any application'
- From the Library on the left, click Utilities, then locate and drag one 'Run Shell Script' from the list of Actions to the large workflow area on the right.
- By default, it should offer to run 'cat', which is what we want. (This unixy utility, which you can also run from the Terminal, simply reads and writes text, but doesn't understand fancy formatting.)
- From the list of Actions, drag a 'Copy to Clipboard' to beneath the 'Run Shell Script' action.
- Save the service from File > Save, naming it something like 'Copy unstyled' or such.
Done. It takes the selected text, runs it through cat and blurts it out on the Clipboard ready to be pasted.
This new service will appear as a shortcut in your right-click contextual menu, by itself or in a Services submenu. And in its real home is in the Application > Services menu. From 'Services preferences' there, you can even assign a global keyboard shortcut for it. Finally, should you want to edit it, you'll find it saved in /Users/yourname/Library/Services/