Résumé
We characterize the finiteness of Gibbs measures for geodesic flows on negatively curved manifolds by several criteria, analogous to those proposed by Sarig for symbolic dynamical systems over an infinite alphabet. These criteria should be useful in the future to find more examples with finite Gibbs measures. As an application, we recover Dal'bo-Otal-Peigne criterion of finiteness for the Bowen-Margulis measure on geometrically finite hyperbolic manifolds, as well as Peigne's examples of geometrically infinite manifolds having a finite Bowen-Margulis measure.