Gollum...

Gollum started following Frodo befor Moria. Gollum is noted, but not yet named, when Frodo and gang are crossing the Brandywine river. Turn to Chapter 5 in FotR, in the 8th paragraph, Sam tells Frodo to look back... "On the far stage, under the distant lamps, they could just make out a figure: it looked like a dark black bundle left behind. But as they looked it seemed to move and sway this way and that, as if searching the ground. It then crawled, or went crouching, back into the gloom beyond the lamps."
We don't know it's Gollum until Moria. I assume he got either through Moria using his sticky fingers and clingy limbs as he scaled up and down mountains and hills further in the journey. Gollum was capabale of much more then we think as the reader. I suspect Tolkien created Gollum with features that would enable Gollum to follow Frodo through everything and anything. Besides, the power of the ring over Gollum and his desire to have it again was a significant symbolism to the story, as much as the struggles the other characters have to overcome and deal with.