To add to the excellent previous answers, Galadriel herself says that some of the Elves may have lingered in Middle-earth, even into our own times.

>"Yet if you succeed, then our power is diminished, and Lothlórien will fade, and the tides of Time will sweep it away. We must depart into the West, or dwindle to a rustic folk of dell and cave, slowly to forget and to be forgotten."

From [Wikipedia][1]:

>After the destruction of the One Ring, the power of the Three Rings of the Elves would also end and the Age of Men would begin. Elves that remained in Middle-earth were doomed to a slow decline until, in the words of Galadriel, they faded and became a "rustic folk of dell and cave," and were greatly diminished from their ancient power and nobility. While the power of the remaining Noldor would be immediately lessened, the "fading" of all Elvenkind was a phenomenon that would play out over hundreds and even thousands of years; **until, in fact, our own times, when occasional glimpses of rustic Elves would fuel our folktales and fantasies.**


  [1]: http://en.m.wikipedia.org/wiki/Elf_(Middle-earth)