What complementary observation campaigns have looked at Kepler's field of view? It seems to be common practice to double up observations. For example, shortly before New Horizons flew by Pluto, several of its moons were discovered by telescopes as a concerted effort was put in because of the occasion.

Have other telescopes made systematic and dedicated observations of the field of view of the Kepler telescope? I imagine speculatively in this paragraph that such observations could've been part of a survey process to determine where to point Kepler out of a set of candidate FOVs to begin with. And once decided upon, that field more closely examined. Then during the Kepler mission persistently observed in order to help rule out noise from passing asteroids and binary and variable stars and to gather complementary data. To characterize transiting planets, it is important to characterize the stars they are orbiting, something which telescopes with other kinds of instruments can be helpful with. Those are just my speculations about why I would think that Kepler's primary mission was "doubled up" by other kinds of telescopes.

What are some of the preparatory, complementary or follow up observation campaigns that have been made of the Kepler field of view? Is Kepler's FOV now one of the most and best observed parts of the sky?
The Kepler Field had been covered in the near IR by the 2MASS catalog since that covered the entire northern sky.  There was also a Smithsonian Institute program called the Kepler Input Catalog program that observed the Kepler field with the 48-inch telescope at the Whipple Observatory on Mount Hopkins, Arizona in the SDSS g, r, i, and z bands plus a custom filter centered on the Mg b lines.  Also many individual objects studied by Kepler were observed in follow up studies.  So, yes this is a well studied region of the sky now.  Now, however, the Pan-Starrs survey has imaged most of the whole sky with several optical filters. 

After the reaction wheel failure on Kepler, it was repurpose as the K2 project.  In this project, it observes a different part of the ecliptic plane every 3 months.  Catalogs of stars and galaxies in each of these locations are created ahead of time with the EPIC survey.  In addition, there is a SN/AGN search ongoing with K2 that includes simultaneous groundbased observations using various wide field imaging telescopes around the world such as the SkyMapper in Australia.  A workshop on this will be held in February.