The EXors are T Tauri stars (TTSs) that occasionally flare up from minimum light, apparently as the result of a massive infall of circumstellar material. The prototype, EX Lupi, is the only example that has been examined spectroscopically in any detail, so this paper surveys what can be gleaned from the literature about five candidate EXors, and describes new observations. The aim is to clarify the nature of these objects, and to determine whether they bear a convincing resemblance to EX Lup itself. The spectroscopy was carried out with the HIRES spectrograph (R = 48,000) at the Keck I telescope between 2004 and 2007. Three of the stars examined are in or near the Orion Nebula (NY, V1118, and V1143 Ori), while V1184 Tau is in the molecular cloud CB34, and V350 Cep is at the edge of the young cluster NGC 7129. The spectrograms were obtained at random times, and there was no coordinated photometry, but it was possible to conclude that the three Orion stars can be considered conventional EXors. At minimum light, they resemble K- or early M-type dwarfs plus a T Tauri-like emission spectrum, but no spectral characteristic was found that set them aside from ordinary TTSs. Such a signature might be found in deep-infrared (IR) photometry, but they do not stand out at 2 μm. Several interesting spectroscopic phenomena were observed, however, notably the appearance of the Li I λ6707 line in emission in V1118 Ori near maximum, and the detection of simultaneous infall and outflow at the Na I D₁₂ lines in several EXors (although that has also been reported in several Classical TTSs). V1184 Tau is not an EXor: it is unclear if its activity is repetitive. Nor is V350 Cep: after recovering from a deep minimum about 1975, it has since remained near maximum for nearly three decades.