There are several choices of minimal, relay-only mail transfer agents (MTAs, or "mail servers"), some of which have been mentioned in other answers:
- msmtp http://msmtp.sourceforge.net/
- nullmailer http://untroubled.org/nullmailer/ (my personal favourite)
- esmtp http://esmtp.sourceforge.net/ (unmaintained)
- sSMTP http://packages.debian.org/source/sid/ssmtp (no longer actively developed)
For either of those to work, you need a full fledged MTA somewhere that will further relay your messages (known as "mail hub") and it is strongly recommended that you control this mail hub. Bad Things™ can happen otherwise.