The email client associated with the GNOME desktop environment is Evolution.
Evolution is a free, open-source personal information manager developed originally by Ximian and now maintained as part of the GNOME ecosystem. It combines email with an address book, calendar, task list, and notes, giving it a role similar to Microsoft Outlook rather than limiting it to message reading and composition.
Evolution became an official part of GNOME with the GNOME 2.8 release in September 2004. It supports common mail protocols such as POP and IMAP for receiving messages and SMTP for sending them. It also supports features including search folders, spam filtering, encryption, digital signatures, and connections to some enterprise collaboration systems.
Geary is another mail application associated with Linux and GNOME technologies, but it is not the traditional GNOME personal information manager named by this question. KMail belongs to the KDE ecosystem, while Thunderbird is a cross-platform Mozilla email client. Ubuntu eventually replaced Evolution with Thunderbird as its default email client in Ubuntu 11.10.