Send from Gmail: Send from Gmail lets you compose messages from your browser without opening Gmail.
Checker Plus for Gmail: Checker Plus for Gmail has many customizable features for keeping you on top of Gmail without having to open your inbox.
Checker Plus for Gmail is free to use, but a donation will unlock extra features.
Inbox When Ready: Inbox When Ready helps you control access to Gmail so you can stay focused on the work at hand.
KeyRocket for Gmail: KeyRocket for Gmail teaches you keyboard shortcuts on the fly.
The free extension tracks your actions in Gmail and lets you know, via pop-up alert, what keyboard shortcut you could have used to complete it.
Source: IT News.