Whether or not you should peel your cucumbers is entirely up to you. There are certain things you lose when peeling a cucumber, such as the high amounts of vitamin K it contains. Because the vitamin K is close to the skin on cucumbers, peeling it off will get rid of most of it.
On the other hand you will also get plenty of vitamin B which has been found in those cucumbers which have been peeled. Some people choose to peel their cucumbers when they get home from the grocery store while others do not. It all depends on what your personal preferences are regarding the nutritional value of them.