Near-infrared photometry and spectroscopy is obtained for a heterogeneous sample of nearby white dwarfs with possible excess flux as identified primarily in the Two Micron All Sky Survey. Among the sample of 43 stars are a number of white dwarfs that are either metal-rich, magnetic, or binary suspects. With a few notable exceptions in four (or possibly five) distinct categories, the newly obtained JHK photometric data fail to corroborate the putative excesses, with K_IRTF - K_2MASS = +0.31 mag. Where available, GALEX photometric data are used to better constrain the overall spectral energy distribution of the white dwarfs, enabling any excess near-infrared flux to stand out more readily against the expected stellar photosphere. With superior data, a near-infrared photometric excess is confirmed at three metal-rich white dwarfs and ruled out at nine others. Several new binaries are confirmed or suggested; five white dwarf - red dwarf pairs and five double degenerates. Four apparently single magnetic white dwarfs -- two DA and two DQp -- display modest to strong near-infrared excess (relative to non-magnetic models), which may be better described as two effective temperatures owing to a redistribution of energy in highly magnetic or peculiar atmospheres.