There are a number of groups who have attempted this throughout history. The Amana colonies in Iowa, The House of David in Benton Harbor, Michigan (both pretty much gone as a group, now), are examples of groups that isolated themselves from the world. Some were utter failures and considered to be bad - Jim Jones' group in Africa, House Davidians (Waco, Texas) are two of the latter.
It should be noted that the Old Order Mennonites and the Amish (a break off group of the same) do not live apart of the world any more than Seventh-day Adventists, Christian Scientists, Catholics, certain Baptist groups, Mormons, Jehovah's Witnesses, all live "apart" from the world in spirit. So do many Christians outside those denominations I've mentioned.
Also any group that sets up and runs convents and monasteries, temples, retreats, and so on.