Create a cell with the value Now().
Format it how you want - like yyyy/mm/dd HH:mm:ss for a full timestamp in 24 hour time.
Now, as long as auto-recalculate (the default) is set, any time another cell is changed, you'll get a fresh timestamp.
Upon further reflection, if you desire a hardcoded timestamp, which is only updated by actions not including such things as open workbook, print, etc. you could create a macro attached to worksheet_change. Set the target cell as text, with specific formatting like before. Use something like:
Sheet1.Cells[].Value = Text(Now(), "yyyy/mm/dd HH:mm:ss") on the Worksheet_Change event.
If you put this into a template that loads at startup, you'll never have to think about it again.
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Possible duplicate of How to insert the =now() function in a cell automatically when I write in another and hit enter
– Raystafarian – 2015-12-10T17:12:45.463@Raystafarian: We've got circular dupes going on. This is the older question. If both get closed, we'll lock out all new answers. – fixer1234 – 2015-12-11T05:38:01.773