We present high-resolution mid-infrared (MIR) imaging, nuclear spectral energy distributions (SEDs), and archival Spitzer spectra for 22 low-luminosity active galactic nuclei (LLAGNs; L bol <~ 1042 erg s-1). Infrared (IR) observations may advance our understanding of the accretion flows in LLAGNs, the fate of the obscuring torus at low accretion rates, and, perhaps, the star formation histories of these objects. However, while comprehensively studied in higher-luminosity Seyferts and quasars, the nuclear IR properties of LLAGNs have not yet been well determined. We separate the present LLAGN sample into three categories depending on their Eddington ratio and radio emission, finding different IR characteristics for each class. (1) At the low-luminosity, low-Eddington-ratio (log L bol/L Edd < -4.6) end of the sample, we identify "host-dominated" galaxies with strong polycyclic aromatic hydrocarbon bands that may indicate active (circum-)nuclear star formation. (2) Some very radio-loud objects are also present at these low Eddington ratios. The IR emission in these nuclei is dominated by synchrotron radiation, and some are likely to be unobscured type 2 AGNs that genuinely lack a broad-line region. (3) At higher Eddington ratios, strong, compact nuclear sources are visible in the MIR images. The nuclear SEDs of these galaxies are diverse; some resemble typical Seyfert nuclei, while others lack a well-defined MIR "dust bump." Strong silicate emission is present in many of these objects. We speculate that this, together with high ratios of silicate strength to hydrogen column density, could suggest optically thin dust and low dust-to-gas ratios, in accordance with model predictions that LLAGNs do not host a Seyfert-like obscuring torus. We anticipate that detailed modeling of the new data and SEDs in terms of accretion disk, jet, radiatively inefficient accretion flow, and torus components will provide further insights into the nuclear structures and processes of LLAGNs.