I'm sorry, but the talk about methane is ridiculous.
As you can see, 18% of greenhouse gas emissions is methane. Of which 40% comes from agriculture. If we assume that all those emissions are from animals farting then that tells us that about 7.2% of global emissions come from animals farting. Of course the real figure is even less than this.
With that in mind, I have an even better question. Methane is CH4 - animals produce it. We know that they do not make it come from nowhere, but also that they do not eat methane. Therefore, where does it come from? The obvious answer is that they must ingest other chemicals that get broken down and produce methane. Hydrogen is obviously found everywhere, especially in water and carbon is found in organic substances. Essentially a very basic explanation is that animals eat carbon (and drink hydrogen in water) and produce methane. The carbon, of course, comes from plants. Plants get their carbon from the atmosphere - they build themselves out of carbon based molecules. So essentially while animals do produce greenhouse gas emissions, if you include their food into the process, they are carbon neutral - they produce carbon into the atmosphere, which is absorbed by the plants, eaten by the animal and the cycle continues.
The greenhouse effect is not happening because of animals farting, it is happening because we're putting carbon into the atmosphere that was locked away and would not have ever got into the atmosphere if it were not for human actions. I'm talking especially about fossil fuels, deforestation and land clearing. These actions all put carbon that was "locked up" into the atmosphere. Those are the actions we need to worry about.