May one use a peeler to peel fruits and vegetables on Shabbos?
Inedible peels: Those fruits and vegetable which majority of people do not eat together with the peel, and it is rather removed and discarded prior to eating, according to all opinions, it is [Biblically] forbidden to use a peeler to remove the peel on Shabbos. This applies even if one intends to do so in order to eat the food right away.
Edible peels: Those fruits and vegetables which majority of people eat together with the peel, some Poskim rule it is forbidden to be peeled using a peeler, and rather may only be peeled with a knife for right away use. Other Poskim however rule it may be peeled using a peeler, and may even be peeled for later use on Shabbos. Practically, those who are stringent are doing a proper act, although those who are lenient have upon whom to rely, and each person is to ask his Rav. [Whenever one chooses to be lenient like the latter opinions one must know in truth that the selected fruit/vegetable is eaten with its peel by majority of people. Thus, cucumbers for example must be verified in each area if it is in truth eaten with its peel by majority of people, as explained next.]
Examples of fruits/vegetables and their peel status: According to the lenient opinion, it is permitted to peel with the help of a peeler apples, tomatoes, pears, apricots, plums, peaches using a peeler. According to all, it is forbidden to peel with a peeler a carrot, orange, grapefruit, Kiwi. The permissibility to peel cucumbers with a peeler is dependent on one’s countries eating habits; if the majority of people are accustomed to eat the cucumber with the peel, then according to the lenient opinion, it may be peeled using a peeler, while if the majority of people remove the peel then it is forbidden to use a peeler according to all.
One who is particular to never eat the peel: If a person is particular to always peel a certain fruit/vegetable, despite it being eaten by majority of people, some Poskim rule that even according to the lenient opinion, one must abide by the Borer restrictions and may not peel it using a peeler and may only peel it for right away use. Other Poskim however rule that it is permitted for him to use a peeler even in such a case.
One who is never particular to remove the peel: All fruits and vegetables that majority of people do not eat with the peel must abide by all Borer restrictions even if the person eating it is personally accustomed to eat the fruit/vegetable with the peel. Thus it may not be peeled using a peeler or any other designated vessel, and may only be done in order to eat right away.
Pesach: Those who are particular not to eat peels on Pesach, and hence peel all their produce, seemingly may still abide by the leniency of using the peeler on Shabbos Pesach for peels that are generally eaten by majority of people, if they are accustomed to follow the lenient opinion during the other Shabbosim of the year.
 See Shabbos Kehalacha Vol. 2 p. 294 and 299-307; Piskeiy Teshuvos 321/34-35
 Iglei Tal Borer 6; Ketzos Hashulchan 125/16; Piskeiy Teshuvos 321/35
 As a peeler is the normal vessel used to remove the peel from a fruit/vegetable and hence is similar to a sieve and sifter, which is Biblically forbidden to be used. [See Admur 319/1; M”B 319/2; Rashi Shabbos 74a]
 The reason: As a peeler is a designated item for separating and negates the required condition of separating with one’s hands. [ibid]
 M”A 321/19 regarding apples; Elya Raba 321/30; Tosefes Shabbos 321/41; M”B 321/84; Orchos Chaim 319/22 in name of Meorei Or; Igros Moshe 4/74 Borer 8; Az Nidbaru 9/10; Chut Shani 25/7
 The reason: As these Poskim hold that the separating prohibition applies to even edible peels and thus when peeling it one must abide by all Borer restrictions, which include not peeling it with a peeler, and even when using a knife, to only do it for right away use. The reason that even edible peels contain the Borer restriction is because when the are peeled off, they are generally thrown out, and hence have a status of Pesoles when one comes to peel it. [Piskeiy Teshuvos 321/34]
 Peri Megadim 321 A”A 30, brought in Shaar Hatziyon 321/97; Iglei Tal Borer 6/12; Shevisas Hashabbos Borer 24 and footnote 45; Kaf Hachaim 321/141; Ketzos Hashulchan 125/16 [see however Ketzos Hashulchan 126 footnote 19]; SSH”K 3/34
 The reason: As according to these Poskim edible peels do not contain a Borer prohibition, as explained above, and hence there is no need to abide by the Borer conditions which restricts one from using a Borer instrument and requires the peeling to be done for right away use. Regarding if the peeler contains an Issur of Muktzah or Uvdin Dechol-see Piskeiy Teshuvos 321/35 footnote 373-374
 Minchas Shabbos 80/69 that it is proper to be stringent when possible, and so concludes: Shabbos Kehalacha ibid; Piskeiy Teshuvos 321/34-35 that it is bets to be stringent when possible, although one who is leninet has upon whom to rely; Michzei Eliyahu 1/51-52; Teshuvos Vehanhagos 1/208
Ruling of Rav Farkash in Shabbos Kehalacha ibid: Rav Farkash rules that one who wishes to be stringent like all opinions [which he rules one initially is to do], is to always apply the separating prohibition to anything being peeled. In a case that one is pressured to peel using a peeler, such as when one has a lot of fruits/vegetables to peel, or in a case that one is pressured to peel the fruits a while prior to the meal, such as in a case that one must leave one’s house now and will only return when the meal will commence, then although one may be lenient like the latter opinions, nevertheless it is proper to also cut off part of the actual fruit together with the peel. [Shabbos Kehalacha 13/9; Piskeiy Teshuvos 321/34]
 See SSH”K 3/34; Shabbos Kehalacha ibid; Piskeiy Teshuvos ibid footnote 363
 Shabbos Kihalacha Vol 2 13 Biurim 2 [p. 300] writes it is proper to be stringent and follow all the separating restrictions. Orchos Shabbos 3/40
 SSH”K 3 footnote 88; See Piskeiy Teshuvos 321 footnote 363
 Piskeiy Teshuvos 321 footnote 363
 The reason: As the peel itself is still viewed as a food, and it is simply due to its Chametz contingency that people avoid it, and not because they suddenly view the actual peel as Chametz or inedible. Accordingly, at the very most they are removing the bad [Chametz] with the good [the peel] of which many Poskim rule is permitted, and hence the leniency would still apply according to the lenient opinion.