Except its no where near as smooth or universal as in Windows. In Linux, you have to worry about KDE programs vs GNOME programs having different clipboards, for example.
Its also why compatible suites of programs (ie: Adobe) can be so useful when those custom formats come into play. Adobe can copy/paste layers from Photoshop and send them over to other programs. If the photoshop layer isn't understood, it seems to become a Bitmap, which works when I'm on a VBulletin forum over in Firefox land.
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Copy/paste works on files / file-managers, images, text, HTML. Yes, any OS could do the same thing, but they largely don't in my experience.