We performed a spectroscopic survey for cometary volatiles with the Infrared Camera onboard the Japanese infrared satellite AKARI. The observations were carried out in the near-infrared wavelength range in the period from 2008 June to 2010 January. In this paper, we summarize the observations and results of the AKARI survey for the mixing ratios of major volatiles in comets. We derived the $2.5-5{mu}m$ spectra of 18 comets including both Oort cloud comets and Jupiter-family comets. Prominent emission bands in the observed spectra are the fundamental vibrational bands of water ($H_2O$) at $2.7{mu}m$ and carbon dioxide ($CO_2$) at $4.3{mu}m$. The fundamental vibrational band of carbon monoxide (CO) at $4.7{mu}m$ and the broad emission feature probably related to C-H bearing molecules can also be recognized around the $3.4-3.5{mu}m$ region in some comets. We detect $CO_2$ in 17 out of 18 comets, and derived gas production rate ratios of $CO_2$ with respect to $H_2O$ in 17 comets. We detect a reliable CO emission band only in three of the comets. Our data set provides the largest homogeneous database of $CO_2/H_2O$ ratios in comets obtained so far.