It works for nether wart, potatoes, carrots, glowstone, melons, and wheat (you get more seeds, not more wheat). I also think when you chop down a tree, you get more saplings/apples, but I think it is most likely false. For all of the crops you get plus 1 I believe.
I've never had any noted difference with the crops,..
Trust me, I tested it about 30 minutes ago. For example, carrots usually drop 4 carrots at max, but I was getting 5 at a time sometimes. It says it on the wiki too, but it says it in a confusing manner. Try testing it out.
Fortune does work on large mushrooms as well as saps and apples. I have the stacks of dark oak saps to attest to that. You can put it on an ax it you want and have the extra fortune 3 or you can use your pick to get the desired amount of saps.