Hierarchical Bayes models are commonly used in Marketing, Political Science, and Econometrics. Yet, the only package I know of is bayesm, which is really a companion to a book (Bayesian Statistics and Marketing, by Rossi, et al.) Am I missing something? Is there a software package for R or Python doing the job out there, and/or a worked-out example in the associated language?
This answer comes almost ten years late, but it will hopefully help someone in the future.
The brms package in R is a very good option for Bayesian hierarchical/multilevel models, using a syntax very similar to the lme4 package.
The brms package uses the probabilistic programming language Stan in the back to do the inferences. Stan uses more advanced sampling methods than JAGS and BUGS, such as Hamiltonian Monte Carlo, which provides more efficient and reliable samples from the posterior distribution.
If you wish to model more complicated phenomena, then you can use the rstanpackage to compile Stan models from R. There is also the Python alternative PyStan. However, in order to do this, you must learn how to use Stan.
Hierarchical Bayes for R or Python