The world's largest living thing is probably a mushroom - Armillaria ostoyae or the honey mushroom. The biggest example of this fungus covers 2,200 acres and is in the Malheur national forest in Oregon. And this mushroom is pretty old too - at least 2,400 years and possibly as much as 7,000 years. (There is some argument that the Pando or quivering aspen of Utah is bigger and older - but it's not a mushroom so who cares!)
I've read mixed reviews on the edibility of honey mushrooms with some claiming them as delicious while others suggest they cause quite serious gastric problems in some people. Personally, I always worry a little about parasitic fungi - no reason to but it some how feels better to think of them as wholly bad!