We present Hubble Space Telescope/Advanced Camera for Surveys (HST/ACS) g and z photometry and half-light radii R h measurements of 360 globular cluster (GC) candidates around the nearby S0 galaxy NGC 3115. We also include Subaru/Suprime-Cam g, r, and i photometry of 421 additional candidates. The well-established color bimodality of the GC system is obvious in the HST/ACS photometry. We find evidence for a "blue tilt" in the blue GC subpopulation, wherein the GCs in the blue subpopulation get redder as luminosity increases, indicative of a mass-metallicity relationship. We find a color gradient in both the red and blue subpopulations, with each group of clusters becoming bluer at larger distances from NGC 3115. The gradient is of similar strength in both subpopulations, but is monotonic and more significant for the blue clusters. On average, the blue clusters have ~10% larger R h than the red clusters. This average difference is less than is typically observed for early-type galaxies but does match that measured in the literature for the Sombrero Galaxy (M104), suggesting that morphology and inclination may affect the measured size difference between the red and blue clusters. However, the scatter on the R h measurements is large. We also identify 31 clusters more extended than typical GCs, which we term ultra-compact dwarf (UCD) candidates. Many of these objects are actually considerably fainter than typical UCDs. While it is likely that a significant number will be background contaminants, six of these UCD candidates are spectroscopically confirmed as NGC 3115 members. To explore the prevalence of low-mass X-ray binaries in the GC system, we match our ACS and Suprime-Cam detections to corresponding Chandra X-ray sources. We identify 45 X-ray-GC matches: 16 among the blue subpopulation and 29 among the red subpopulation. These X-ray/GC coincidence fractions are larger than is typical for most GC systems, probably due to the increased depth of the X-ray data compared to previous studies of GC systems.