In Notepad++, how can I insert the current date and time?

If your Notepad++ shipped with TextFX, you can find this in TextFX > TextFX Insert > Date & Time - short format, which will insert a string in the exact same format. If you don't see a TextFX menu, install it via the plugin manager and it will appear.

You can then bind it to a keyboard shortcut in Settings > Shortcut Mapper... > Plugin Commands. Look for I:Date & Time - short format in the mappings.

Step 1 : Install plugin TextFX
Step 2 : Insert Date & time