Gmail Checker is a simple Chrome extension that alerts you to incoming e-mails.
Gmail Checker installs itself as a small mail icon next to the URL or address bar of your browser. If you have unread emails. it alerts you instantly and shows the number of unread messages as a number on the icon. If you click on the mail icon, the browser opens the Gmail inbox. However Gmail Checker isn't much more advanced than that - there are no preferences and there's no support for multiple accounts.
Gmail Checker is a simple add-on although there are very few advanced options.