I am aware of a few density estimation methods. I think that this paper is a good reference Density estimation in R

In the past I have used average shifted histogram and KernSmooth for density estimation. I am curious what methods are are good fit for Stan? How do Stan users estimate non-parametric densities.

Bayesian density estimation, or more generally Bayesian nonparametrics, typically involves priors on distributional spaces (Dirichlet processes or in some cases gaussian processes). I would check out Ch 23 of BDA. I personally do not have any experience with implementing them in Stan – my brief impression is that it will probably be difficult to do a ‘true’ Dirchlet process with HMC sampling.