I see situations where you may have to input the same password more than once. You may type it in a text editor and copy it to clipboard, to paste it two or more times.
In what scenarios this could be a bad idea?
The Windows clipboard is not secure.
This is a quote from a MSDN article.
The Clipboard can be used to store data, such as text and images. Because the Clipboard is shared by all active processes, it can be used to transfer data between them.
This should probably apply to Linux machines as well.
Is this a concern? No. For someone to exploit this, he would have to have malware on your machine capable of reading data from the clipboard. If he has the capability of getting malware on your machine, you have much bigger things to worry about as there are plenty of other stuff he can do, including keyloggers and the like.
Aside from the clipboard contents being available for snooping, there have been exploits where web pages can grab your clipboard data, and one where web ads written in Flash (this was before version 10) could stuff malware URLs onto your clipboard, in hopes that unsuspecting users would paste them into e-mail, blogs, etc., without noticing what they contained. Since my clipboard extender (ClipMate) acted as an early-warning to the malicious activity, my blog post was cited quite a bit.
This is insecure; as the MSDN article notes, the data can be read by other users (and by unprivileged users). Someone who could not necessarily install other malware could still read the clipboard data.
When it would be a "bad idea" depends on what might be running on the system, how sensitive the password is, etc.