Why exactly do we need a "Circular Linked List" (singly or doubly) data structure?

A simple example is keeping track of whose turn it is in a multi-player board game. Put all the players in a circular linked list. After a player takes his turn, advance to the next player in the list. This will cause the program to cycle indefinitely among the players.

To traverse a circular linked list, store a pointer to the first element you see. When you see that element again, you have traversed the entire list.

void traverse(CircularList *c) {
  if (is_empty(c)) {
    return;
  }
  CircularList start = c;
  do {
    operateOnNode(c);
    c = c->next;
  } while(c != start);
}

Two reasons to use them:

1) Some problem domains are inherently circular.

For example, the squares on a Monopoly board can be represented in a circularly linked list, to map to their inherent structure.

2) Some solutions can be mapped to a circularly linked list for efficiency.

For example, a jitter buffer is a type of buffer that takes numbered packets from a network and places them in order, so that (for example) a video or audio player can play them in order. Packets that are too slow (laggy) are discarded.

This can be represented in a circular buffer, without needing to constantly allocate and deallocate memory, as slots can be re-used once they have been played.

It could be implemented with a linked-list, but there would be constant additions and deletions to the list, rather than replacement to the constants (which are cheaper).

Applications

1) We can use circular linked list any application where the entries appear in a rotating manner.
2) Circular linked list is the basic idea of round robin scheduling algorithm.