What Beers are Brewed with Wild Yeast? Is this practiced commercially? I'm not sure if it would scale very well, because I understand that the technique takes a long time even for a home brew batch. 

If so, what beers are brewed using this technique and why? Is it specific types of beer, or specific brewers, perhaps going for the "organic" angle?
Belgian Lambics are probably the most notable beers brewed with wild yeast. They are fermented in open vats, and wild yeast strains specific to the area contribute a very distinctive flavor to these beers. Lindeman's is probably the best known commerical example in the US, although these beers are sweetened and are not usually considered a true example of the style. 

There are strains of wild yeast that have been cultivated for commercial use such as Brettanomyces. Breweries use this yeast to produce sour flavors via lactic acid production. Brewers will use it both in primary fermentation, and by aging their beer in barrels that have been "infected" with it.