Can a browser get the data on my clipboard? Data could be for example my temporary password?
Any browser or operating system that allows this?
In Tools -> Internet Options -> Security -> -> Custom Level, you can find the following setting:
Sadly, I wasn't able to find an equivalent setting in neither FF nor in GChrome.
On Windows, any process (running on the same desktop, IIRC) can monitor changes to the clipboard with the SetClipboardViewer API call.
PasswordSafe, a well known password management tool, allows you to drag and drop the password onto a web page, bypassing the clipboard altogether.