Let's say, you want to send an email to user@example.org but you accidentally wrote user@exmaple.org (spelling error), then Gmail will most likely save the email for future reference.
However, when you send your email, an email pops up in your Inbox saying "Mail Delivery Notification (Failure)" of the incorrect email address you used. You now notice your mistake, and go and compose a new email with the correct email into your "To" box, but you notice that the incorrect email address comes up as a suggestion! How to get rid of it?
Best Answer
If you go into your Contacts, for instance in Gmail, there is an option called 'Other Contacts (#)' on the menu provided. If you select that and search for the incorrect email (that you don't want to show up in your suggestions), select it, press the 'More' button at the top-center of the page, and then scroll until you see 'Delete'.
Now, you must give Gmail time to process the information (1-2 minutes), so sign out of your email. Sign back in after some time, and test-trial to see if the incorrect email still appears in the suggestions box. It shouldn't.
This answer is by NikO; I moved it to the answer box.