It is important to detect floating oil slicks after spill accidents, and hyperspectral remote sensing technology is capable of achieving this task. Traditional methods mainly utilize the spectral indices of hydrocarbons to detect floating oil slicks, but are poor at distinguishing the thickness of oil slicks and cannot detect sheens. Since the spectra of oil slicks should be affected by seawater as well as oil, this paper investigated the use of spectral indices of hydrocarbons and seawater to identify different thicknesses of oil slicks. In this research, a measurement, called index separability (IS), was proposed for quantitatively evaluating the identification ability of these spectral indices. Based on the evaluation results, experiments were conducted to validate the applicability of these spectral indices. The results show that the spectral indices of hydrocarbons are more suitable for detecting continuous true color oil slicks and emulsions and that spectral indices of seawater are more suitable for sheens and seawater. In addition, the spectral indices of hydrocarbons and seawater are complementary for detecting oil slicks. Finally, combining the spectral indices of hydrocarbons and seawater is conducive to achieving more accurate oil slick recognition results.