Tiny enough to enter living cells, the Nanites were seen on episode No.50 "Evolution" when microscopic robots (accidentally evolved in intelligent life-forms) got into the circuitry of the starship USS Enterprise-D after escaping from an experiment conducted by Ensign Wesley Crusher (Wil Wheaton) in the year 2366.

The Nanites (who could be destroyed with a burst of high-level gamma radiation) were eventually transferred to the Kavis Alpha IV where they founded their own civilization.

Nanites were also considered as a possible solution for destroying the Borg when they attacked Earth on episode No.75 "The Best of Both Worlds, Part II."  

TRIVIA NOTE: Similar creatures called Replicators (tiny self-replicating machines) appeared on the sci-fi series STARGATE: SG1 and STARGATE ATLANTIC. They were first mentioned in the episode "Fair Game" and first appeared in the episode "Nemesis."

The Replicators were created by Reese (Danielle Nicolet) an advanced gynoid, built by a scientist.  Her systems are maintained by millions of nanites (nanobots) which are able to reorder matter on a microscopic level. The Replicators eventually evolved into a race of humanoids which threatened the galaxy and beyond.