If you try pasting into Word-Pad, Notepad++ or Word you wouldn't have this issue. To copy the cell value as pure text, to achieve what you describe you have to use a macro:
In the workbook where you want this to apply (or in your Personal.xls if you want to use across several workbooks), place the following code in a standard module:
Code:
Sub CopyCellContents()
'create a reference in the VBE to Microsft Forms 2.0 Lib
' do this by (in VBA editor) clicking tools - > references and then ticking "Microsoft Forms 2.0 Library"
Dim objData As New DataObject
Dim strTemp As String
strTemp = ActiveCell.Value
objData.SetText (strTemp)
objData.PutInClipboard
End Sub
To add a standard module to your project (workbook), open up the VBE with Alt+F11 and then right-click on your workbook in the top left Project Window and select Insert>Module. Paste the code into the code module window which will open on the right.
Back in Excel, go Tools>Macro>Macros and select the macro called "CopyCellContents" and then choose Options from the dialog. Here you can assign the macro to a shortcut key (eg like CTRL+C for normal copy) - I used CTRL+Q.
Then, when you want to copy a single cell over to Notepad/wherever, just do Ctrl+q (or whatever you chose) and then do a CTRL+V or Edit>Paste in your chosen destination.
My answer is copied (with a few additions) from: here
EDIT: (from comments)
If you don't find Microsoft Forms 2.0 Library in the references list, You can try
C:\Windows\System32\FM20.dll
(32 bit
Windows) (thanks @JWhy)C:\Windows\SysWOW64\FM20.dll
(on 64-bit)