Known MicroRNA - Gene Systems?
Yes. Below is a link to a review of ncRNA (non-coding RNAs) and their role in disease. There are many examples in this review in all sorts of diseases, one of which is miR-200, which is thought to play a role in some cancers. 

There are also some tables in the paper that list the miRNA and the disease they are linked to. They also have a reference for each one, so you could read more about that particular miRNA and its function, including the gene it regulates.

http://www.nature.com/nrg/journal/v12/n12/full/nrg3074.html

Im not sure if that article is open to the public or not. If you cant access it you could always check out the wikipedia entry for miR-200

http://en.wikipedia.org/wiki/Mir-200