How much gas does a cow produce in its lifetime?
Although the amounts vary from cow to cow depending upon many variables, including the quality of the feed given to the animals, a dairy cow cranks out about 142 kilograms of methane per year. (The U.S. EPA says it's more like 100 kg/yr.) Beef cattle don't fart as prolifically, squeezing out only about a little more than half as much methane, 76 kg/yr.
Note that those figures DO NOT take into consideration the amount of methane produced by the decomposition of manure.
Just to be clear, cattle and other ruminants release methane primarily by belching. It is a common misconception that cows are monstrously flatulent.