Already being done on small scales. Dairy farmers all over the place do it with their manure piles for power generation to reduce their energy costs.
But while you're capturing all that methane and thinking you're doing a good job for the environment, every time a "green" hydro-electric dam is built you create a whole new methane source. Three Gorges Dam is a great example of that.
Don't know why you haven't yet heard about methane landfill gas capture..been around for years..