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);
}