Clipboard not working
From MozillaZine Knowledge Base
This article describes why the clipboard (Cut, Copy, Paste) may not work.
Clipboard never works
If the clipboard never works, you are probably being affected by malware, or some other application that uses a specific registry string, AppInit_DLLS at HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows NT\CurrentVersion\Windows. There have been some reports that this string simply existing can cause the problem, without pointing to a specific application. The most commonly reported applications that this string points to are the pushow malware and Google Desktop. The Copernic file system search application is also said to cause the issue.  If the string points to a legitimate application, removing it might cause the application to stop working. Reinstalling the application afterwards may fix it, or it may recreate the string and the problem. Not everyone who has this string in their registry has a clipboard issue.
Caution: While these steps should be safe to perform if followed correctly, you should never edit the registry if you don't feel confident or are unsure of what you are doing.
Pushow (pop up show), a malware, affects the clipboard through AppInit_DLLs. (See Bug 334500.) Infected computers have files "popupshow.dll" or "pushowxx.dll", where "xx" is a random number, within "C:\Windows\System32\". To check for infection, Windows users should enable "Show hidden files and folders", search for "pushow*" and "popupshow.dll" files, and delete these files. Deleting these files is not usually possible until AppInit_DLLs is removed. Anti-malware software may not detect pushow, even if the software's definitions are up to date. 
New.net is malware that installs itself on Windows machines as a Firefox extension when certain other applications are installed onto the system. New.net is meant to allow the user to access new.net-specific addresses, but it also interferes with the clipboard. It can't be uninstalled from within Firefox.
New.net was providing a removal tool, however, note that as of 30. August 2009, the link doesn't work anymore; to get rid of it use one of the methods provided on these websites. New.net malware can also be removed with anti-spyware programs such as Spybot or Microsoft Anti-Spyware.
Applications that bundle New.net
Clipboard stops working sometimes
Opening multiple windows using a desktop or quick launch shortcut can cause a focus bug which breaks clipboard tasks, and other focus dependant tasks, especially in text fields (Bug 220900). Minimizing the windows and maximizing them will usually reset focus once this issue is encountered. To avoid seeing this issue altogether, launch new windows using the New Window menu item, or short cut (Ctrl+N) or add a New Window button to your toolbar. There is currently a patch waiting for testing and landing to fix this issue.
Rich text editors
If Copy/Paste doesn't work only in rich text editors (such as those used by GMail or Yahoo! Mail), read this article.
Microsoft Remote Desktop
Using Microsoft Remote Desktop can break the copy/paste feature. Shutting down the remote desktop restores the functionality.
Inspecting clipboard contents
To see what's actually on the clipboard, you can use utility tools provided by your operating system. On Windows, run CLIPBRD.EXE from the command line (DOS prompt) or Start → Run. Its View menu allows you to inspect in which "flavors" the content is available and to switch between different representations. On Linux with KDE, use Klipper to see what's on the clipboard.
Mozilla applications can handle unformatted (plain text) and HTML encodings. Note that RTF (rich text format) is currently not supported.
For images, the only format accepted on Windows is "Device Independent Bitmap" (DIB), whereas Linux and Mac should support JPEG and PNG encodings, as well as GIF if provided.
Related bug reports
Try the standard diagnostic.