I wasn't kidding when I tell you that I have almost every kitchen tool or gadget you can think of. I've pooled together all of the peelers I could find, because, yes I really do use all of them. In the photo, you'll see a variety of peelers, but I think in the real world you could find many other kinds in addition to these.
So when do you use which peeler!? Well, I use the traditional peelers for carrots and potatoes. You don't need anything fancy (2nd from left AND the last one on the right). In fact, using a fancy peeler on something so small really makes the job harder. For example, if I were to use the peeler 2nd in from the right on a potato, I might end up cutting my wrists. It's just not worth it. However, I do use that particular peeler for peeling eggplant. It allows you to hold the eggplant with one hand and since it is long enough, you start from the top and peel toward you. Much easier than using a knife and the traditional peeler, in the end, use it to peel long vegetables.
Also, the wooden handle is an apple corer/some kind of peeler. Pretty neat eh? I am sure at one point it was, but the peeler is too dull for apples, maybe its ok for carrots, and MAAAYBBBEEE if you are creative you can use this one to make neat garnishes (which I haven't mastered yet, but one day!)
What is that strange looking one all the way to the left? Ohh...that is a citrus zester! It allows you to peel the skin of a citrus, so if a recipe calls for lemon zest, this baby is your tool. It peels in strips and just deep enough to get all of the mouth watering flavors while avoiding the horridly bitter white pith (the white membrane between citrus peels and the actual fruit). I seriously use this ALL the time, its much easier than using a grater.
I think that about sums it up. I hope you were able to follow the puzzle which is my rambling on, but I do also hope you've learned something helpful. And, no recipe today mehhhh!