If you’re using a Gmail or iCloud account in the iOS Mail app, you actually have the option of choosing to have the standard Trashcan button either delete messages or archive them.
While the default behaviour for the button can be configured in the Mail account settings to archive instead of delete—in which case it will display as an archive bin rather than a trashcan—you can also override the behaviour on a per-use basis simply by tapping and holding your finger on the button for about a second; a pop-up menu will appear with both Delete and Archive options available.
This works when viewing an individual message as well as when performing an archive or delete operation on multiple messages.