We have studied the gas-phase reactions of CF+ with 24 neutral species. Reaction rate constants and product branching fractions are measured at 298 K using a flowing afterglow-selected ion flow tube. Experimental work is supported by computational chemistry calculations to provide insight into the reactivity of classes of neutral molecules. Reactions of CF+ with small triatomic species and oxygen-containing organic molecules produce the stable molecule CO. The product branching fractions are discussed, and the potential energy surfaces for a few representative reactions are examined. CF+ is highly reactive with complex molecules and will likely be destroyed in dense environments in the interstellar medium. However, the lack of reactivity with small diatomic molecules will likely enable its survival in diffuse regions.