I normally install postfix for my MTA. However, I've never really used sendmail so I'd decide to give it a whirl for a new application I'm working on. I don't use it for anything but handling the mail that the application needs to send out, like new user welcome emails, password resets, etc.

apt-get install sendmail

Sendmail, unlike postfix, won't work out of the box. Postfix will prompt you for the necessary config setup when running the install. Sendmail won't, and therefore it's not 'out of the box'. You'll have to make some modifications on your own. Nothing major but this is what I've found in order to get it to work, reliably and quickly. The first thing I did was add the fully qualified domain name to my /etc/hosts file

#vim /etc/hosts
127.0.0.1 www.mydomain.com

After this I added the fully qualified domain name to my apache default configuration file

#/etc/apache2/sites-available/default
ServerName www.mydomain.com
#vhost info etc...

Reload and restart...

/etc/init.d/apache2 force-reload
/etc/init.d/sendmail restart

You can test sendmail like so

sendmail email@example.com
hello
from
me
.

This should deliver a message to you (the "." on a new line, followed by a new line, closes the message).

Just finishing up brewing up some fresh ground comments...