I'm a previous owner of littermaids, and while they work ok, they do suffer from the problems listed by many others...they are noisy, get stuck, make a mess, are a mess to try to clean, and have expensive waste containers. I even remember a time where I was trying to get containers from them for almost 3 months. Seemed they were having problems with their supplier in Hong Kong if I remember correctly. Still, it was better than the old methods in many ways.
The Litterfree seemed to offer the ideal solution...on paper, that is. Yet most users report that even if they get their cats to use it, it has a lot of problems. In fact, it sounds like more of a pain in the you know what than the Littermaid.
Litter Robot sounds like the best product on the market...at the moment. If you go to their website and look at the testimonials, there is at least one link to a magazine reviewer that compared the item to his Littermaid...favorably too.
What I think best sums it up is the classifieds. It is no surprise there are a lot of Littermaids for sale, new and used, as they have been around for many years now. Litterfree units and Litter Robots have been around for approximately 2 years, and while you can find Litterfree units for sale used (usually with an explanation that a cat refused to use it), there isn't a single Litter Robot available. Check ebay. I think I'm going to try the Litter Robot.

