Many years ago, this was sometimes due to the "rdpclip" utility not being properly installed. But with newer versions of Windows, installing rdpclip should not be required.
So, if you can't get copy and paste to work with your RDP session, here are two possible causes.
Open the RDP connection properties.
Select the Local Resources tab
Make sure that Clipboard is checked

Even though Clipboard is checked, copy and paste may still not work properly.
If that is the case, click on the More button at the bottom of the Local Resources tab.
Make sure that at least one of your local drives is checked. Apparently the clipboard feature requires access to a local drive to transfer the clipboard data, even for text.

If you have verified both of these settings on your RDP connection, then it could be that the server has disabled clipboard mapping or drive mapping in the Terminal Services Configuration utility.

In that case, you can try and inquire with the system administrator to see if you can have those options enabled.
I'm guessing there are probably a few other reasons why copy and paste will not work, but these are the ones I've run into most frequently.
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