I was having a google search for robots using linear motors, and I only found a few examples of industrial/experimental robots. Indeed, the Wiki page on linear motors doesn't mention linear motors being used for robotics at all - only monorails and railguns.
So I thought I'd find some people who know about robotics. I thought that linear motors would be perfect for replicating human or animal motion, because it's straight out linear like a muscle, rather than converting rotary motion. Plus, if one simply pulls, then two on either side of an arm can act sequentially like how muscles work. Apparently, linear motors tend not to be powerful though, and I'm not sure why.