Fortunately, a little tweak in Gmail's settings puts label and unread count in the browser title bar's front so they're visible in all but the very shortest background tabs and minimized windows.
Make the Gmail Unread Count More Visible in Tabs
To move the unread count forward in the Gmail page title and make it visible in background tabs or collapsed and minimized windows:
- Select Settings in Gmail.
- Go to the Labs tab.
- Make sure Enable is selected for Title Tweaks.
- Click Save Changes.