Zen is perhaps the most well-known Drupal theme, created and maintained by the also well-known John Albin. It’s a lightweight, mobile-first responsive base theme with Sass/Compass support and very few opinions about how you should be doing things.
At around 111,000 reported installs at the moment, Zen is also almost twice as popular as Omega, which is in the number two spot. This means that you get a big community of users answering questions, writing documentation, and fixing bugs along with some battle hardened code that other base themes can’t match.
Why has it been so popular? For one, Zen has been around for a long time. It was first created back in 2006, making it a good bit older than just about all other base themes still being maintained.
It is known as one of the most accessible base themes, and the maintainer has done a lot of work in this regard. Plus, it has RTL support.
Zen has also done a good job of balancing tried-and-true, rock-solid solutions with the cutting edge of frontend development. For example, it picked up Sass/Compass back in 2011, well before most Drupal themers were thinking about it, but it has stayed away from all the fancy plug-ins that might not be widely used or officially supported.
Besides that, it’s the brainchild of John Albin, a highly respected member of the Drupal community. You can rest assured that John Albin isn’t going to lead you astray.
All that being said, to me the big draw of Zen is ...