Edwin's answer of using PPA is great. But if you like being adventurous You can try building from source too.
Download the source
wget -c ftp://ftp.mutt.org/pub/mutt/mutt-1.7.0.tar.gz
Extract it and cd to it
tar xf mutt-1.7.0.tar.gz
cd mutt-1.7.0/
Make sure you have necessary development packages installed. I had build-essential installed already and needed to install libncurses5-dev. So do this
sudo apt-get install build-essential libncurses5-dev
Then proceed with installation. You should check the INSTALL file customize the build. For example you might want to use these parameters to configure
--enable-pop for enabling POP3 support
--enable-imap for enabling IMAP support
--with-ssl which will enable SSL support for POP and IMAP. Needs OpenSSL headers and development libraries.
Now the typical sequence of commands. (If you want customizations, you'll need to pass the options after ./configure like ./configure --enable-pop.)
./configure
make
sudo make install
or if you want to use checkinstall the last step would be
sudo checkinstall -D make install
the -D switch is used to make a debian package from installation. Check details on it in the Addition section.
Mutt 1.7 should get installed.
Addition: As andrew.46 said, we can also use checkinstall instead of make install. This will give us the opportunity to remove the package with a single command and to have a debian package (if -D option is used), which can be used in multiple other machines to install it.
More on checkinstall