Although it is (relatively) easy to use something like Jenkins for Continuous Integration with Drupal, you can create something of a dumbed-down budget version with just four commands:
- svn update (or svn switch, or git equivalents)
- drush updatedb -y
- drush features-revert-all -y
- drush cc all
To put that in plain English, this will:
- update to the latest code base from SVN/GIT, etc
- run any database updates in _update() functions
- update to the latest version of any enabled features modules
- clear all caches so that the latest feature changes are applied
The key to this is a disciplined use, and good understanding of features in Drupal 7. I usually try to use a number of relatively small, well-defined feature modules, rather than one over-sized one.
If you are just looking for a way of rapidly deploying in an automated, reliable and repeatable way, this may well be sufficient for you. If you need more CI-related features such as automated testing, code review, automated code documentation, etc. then you'll probably still need something like Jenkins.