Run bleach through it regularly, very diluted bleach of course or you will kill the hoses/plastic and leave a residue with a bleachy good taste

This problem is why virtually no restraunts use open handles ice machines anymore (the old kind with the big hatch and you reach in and scoop out the ice) because you need to clean them several times a day and the health inspector will bite you in the rear everytime. Most places with their act together use ice dispensers (push the button here comes ice) becuase you can just run diluted bleach through it once a day as part of the cleaning cycle and the constant cycle of movement lessens the chance of mold buildup, whereas a bunch of ice sitting together in one place gives you mold mold mold.

I'm assuming you are talking about a built in machine in your firidge, in which case you may need to interrupt the water line and run the bleach through it, unless you have a removable unit. Also, cycle it more if the ice reservoir is small, and throw a lot of ice out, like once a week run it unitl its dry to help flsuh all the critters out