Is there an application for reading mobi files?
calibre 
Overview
calibre is a free and open source e-book library management application developed by users of e-books for users of e-books.
Calibre is primarily a ebook cataloging program. It manages your ebook collection for you. It is designed around the concept of the logical book, i.e. a single entry in the database that may correspond to ebooks in several formats. It also upports conversion from a dozen different ebook formats to LRF and EPUB. A graphical interface to the conversion software can be accessed easily by just clicking the "Convert E-books" button.
Supported input formats are: MOBI, AZW, LIT, PRC, EPUB, ODT, HTML, CBR, CBZ, RTF, TXT, PDF and LRS.
Starting calibre's ebook viewer as a standalone application
In certain cases you will not want to add an epub or mobi file to calibre's library before reading it. Luckily calibre's ebook viewer can be started independently via ebook-viewer. This makes it possible to create a standalone launcher:
#!/usr/bin/env xdg-open
[Desktop Entry]
Version=1.0
Type=Application
Terminal=false
Icon=calibre
Exec=ebook-viewer %f
Name=Ebook Viewer
Comment=Display .epub files and other e-reader formats
StartupWMClass=ebook-viewer
MimeType=application/x-mobipocket-ebook;application/epub+zip;
See here for more information on adding launchers to your system.
To click an ebook and open in ebook-viewer, make this application (usr/bin/ebook-viewer) the default for that type of file.
Use FBReader, which is available as 'Ebook Reader' in the Software Center (fbreader in Synaptic Manager). Less bulky than calibre.
It can open a variety of ebook types, including 'azw'.
To open ebook on single/double click, the executable file to be added is usr/bin/fbreader.
Another option is Okular.
You also need the kdegraphics-mobipocket package.
sudo apt-get install okular kdegraphics-mobipocket