Which LMS do you use and why?

I use Accord LMS.   This is an incredibly powerful and flexible learning management system.  The best part - this is relatively inexpensive for the power and feature set it delivers.   It's also pretty straight-forward to set up.

It's based on a DotNetNuke platform which is a free,open-source content management system.   It's fully SCORM compliant and allows us to host any kind of content I choose.  The report features allow me to track hundreds of different aspects of client data.  And because it's based on DNN, user access can be tightly controlled so that I can have multiple clients with their users securely accessing only their content.  I currently have about 20,000 concurrent users across about 3 dozen client companies.   

Another nice aspect of this LMS is you can easily integrate it with an eCommerce module if you want to sell your learning content.   There is also a nice Forum module which I use closely with the elearning content.   And you can generate Certificates of Completion pretty easily as users complete learning events.