Free Mac app MailTab is worth the price of admission just for its notifying capability. In addition to alerting you to the arrival of new e-mail messages, MailTab provides a resizable drop-down window that let's you quickly access a mobile view of Gmail from your Mac's menu bar.
After installing and launching MailTab and signing into your account, you'll be able to click on the MailTab envelope icon in the menu bar to peruse and search your inbox, respond to old and compose new e-mails, and star certain messages. The app feels smooth and responsive, but it lacks support for multiple accounts, which will be a big drawback for many Gmail users. Another drawback: the app displays a small ad at the bottom of the drop-down window.
For a single account, however, MailTab is a useful tool for quickly glancing at your inbox without opening a browser. I have my Gmail inbox constantly open in a pinned tab throughout the day, so I doubt I'll use MailTab for responding to e-mails and composing new messages. I may still use it, however, strictly to notify me of new messages. In MailTab's settings, you can select from three notification types: Red Icon, Beep, or Popup. The Red Icon option turns the black envelope red in the menu bar, Beep plays a sound of your choosing, and Popup displays a Mountain Lion notification window.
MailTab is free, but there's a handful of upgrades. You can remove the ads for 99 cents, get desktop mode with chat for $1.99, gain opacity control for 99 cents, or get all three for $2.99.