Frodo and Sam
"We're going round in circles."
Frodo

Frodo and Sam leave their companions at the Falls of Rauros and enter the Emyn Muil, an impassable labrynth of jagged rocks and ravines. The Ring is beginning to take an even greater hold on Frodo, weighing him down and tiring him out, the tangle of rocks which they are trying to get through doesn't help. Not surprisingly they soon find themselves going round in circles and despite the fact that they can see exactly where they want to go, the hobbits can't seem to find a way to get there.
One day as they are travelling their path leads them straight over the edge of a small cliff, luckily for them Sam picked up some Elvish rope when they were in Lothlórien and though it is thin, it's very strong. Strong enough, in fact, to carry two hobbits down to the ground. For a while Sam is upset about leaving such a fine rope behind, until he tugs on it and the whole thing comes tumbling down.
Another reason why the hobbit's weren't too keen on leaving the rope behind was because for some time since they'd entered the Emyn Muil they had the feeling that they were being followed, although it was difficult to be sure who it was, as the creature was sneaky and would disappear in an instant. Frodo and Sam hoped that their pursuer would not be able to follow them down the steep cliff and so would give up the chase. But Gollum could not be lost so easily.