There are a few ways to work around this, depending on what you want to do with the data you're holding.
If you're using these Notepad windows as holders for text that you want to copy-paste into other applications, you could use a 3rd party clipboard manager to manage the stack for you.
If they're simple to-do items, you could consider using the included Sticky Notes feature. They will, however, persist through restarts etc. until you delete them. On the plus side, they won't take up space in the taskbar.
If you absolutely must use Windows Notepad for some reason, then there are window-management and macro utilities that you could potentially set up to auto-press "don't save" when the prompt appears. This is the hackiest solution.
If none of these apply, or you just prefer to have a large space to work with your text, then it's probably time to upgrade to Notepad++ (it's free!) This answer will show you how you can configure it to persist your session so that it will never ask you to save open files, which is almost what you want. Similar to sticky notes, the open files will persist until explicitly closed. Using a new editor also comes with the benefits of more powerful features, and the ability to use tabs for your multiple documents.
I would recommend using Notepad++ over the other options, but if you want to provide a more specific use case, then please leave a comment!