Most regression packages support estimation of cross-section Poisson and negative binomial regression models. Packages that claim to have a significant component for count models most likely cover cross-section truncated, zero-inflated, and hurdle models, and they may cover the standard panel count models. Packages that instead only include counts within a GLM module do not cover truncated, zero-inflated, and hurdle models and only cover panel counts to the extent that they have GEE and generalized linear mixed model modules. They do not cover the Poisson fixed effects model.
LIMDEP 9.0 covers a wide range of cross-section count models, including censored, truncated, hurdle, zero-inflated, latent heterogeneity, and latent class, as well as panel fixed and random effects Poisson and negative binomial.
Stata 12.0 covers a similar range of models. Additionally it covers GLM and GEE estimators, some mixed models, and a wide range of mixed models with user-written add-on GLLAMM.
SAS 9.3 covers a similar range of models to Stata through procedures COUNT, TRCOUNT (a recent addition that covers zero-truncated and panel), GENMOD, GEE, and NLMIXED. Procedure COPULA covers copula-based models.
EViews 7.2 covers cross-section Poisson, NB, and GLM.
TSP 5.1 covers cross-section Poisson and NB. It also provides a relatively simple syntax for ML and GMM estimation of user-provided objective functions, including panel count models.
SPSS 20 covers cross-section Poisson and NB and has procedures GENLIN, GEE, and GLMM for GLMs and their multi-equation extensions.