The usual explanation books give for cloudy stock is that you let it get to a full boil rather than a very mild simmer--just an occasional bubble or two. This emulsifies some fat into the stock, causing cloudiness. I generally run it through my chinois, which is not as fine a screen as cheesecloth would be.
Freezing it and thawing it also seems to help reduce cloudiness, though probably not as much as the other two methods.
If I"m making potato soup, it doesn't matter whether its cloudy or not, the soup isn't clear. For chicken soup, it depends on whether or not I add noodles or dumplings, both tend to cloud up the stock. It seemed to me that the onion soup I made a week ago got a little clearer after I added in the onions and the sherry, not sure why.
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