We have conducted a homogenous near-IR spectroscopic survey of 33 objects with varying degrees of similarity to FU Orionis.Common spectroscopic features that are characteristic of the three classical FUors FU Ori, V1057 Cyg, and V1515 Cyg are: strong CO absorption, weak metal absorption, strong water bands, low gravity, strong blue shifted He I absorption, and few (if any) emission lines. Based on these criteria, we classify the 33 objects as either bona fide FUors (eruption observed), FUor-like objects (eruption not observed), or peculiar objects with some FUor-like characteristics, and present a spectral atlas of 14 bona-fide FUors, 10 FUor-like objects, and 9 peculiar objects. All objects that we classify as FUors or FUor-like have very similar near-IR spectra. We use this spectral similarity to determine the extinction to each source, and correlate the extinction to the depth of the 3 µm ice band. All bona fide FUors still today maintain the spectrum of a FUor, despite the eruption occurring up to 80 years ago. Most FUors and FUor-like objects occupy a unique space on a plot of Na+Ca vs. CO equivalent widths, whereas the peculiar objects tend to be found mostly elsewhere. Since most FUors show a reflection nebula, we also present an atlas of K-band images of each target. We found that the near-IR spectra of FUors and young brown dwarfs can be extremely similar, a distinguishing feature being the Paschen β absorption in the spectra of FUors. Although V1647 Ori, AR 6a, and V346 Normae had been previously classified as candidate FUors, we classify them as peculiar objects with some FUor-like properties since their spectra now differ significantly from bona fide FUors. We confirm two new FUor-like objects that were initially identified as candidates based on their near-IR morphology.