Simulations in neuroscience are performed on local servers or High Performance Computing (HPC) facilities. Recently, cloud computing has emerged as a potential computational platform for neuroscience simulation. In this paper we compare and contrast HPC and cloud resources for scientific computation, then report how we deployed NEURON, a widely used simulator of neuronal activity, in three clouds: Chameleon Cloud, a hybrid private academic cloud for cloud technology research based on the Open-Stack software; Rackspace, a public commercial cloud, also based on OpenStack; and Amazon Elastic Cloud Computing, based on Amazon’s proprietary software. We describe the manual procedures and how to automate cloud operations. We describe extending our simulation automation software called NeuroManager (Stockton and Santamaria, Frontiers in Neuroinformatics, 2015), so that the user is capable of recruiting private cloud, public cloud, HPC, and local servers simultaneously with a simple common interface. We conclude by performing several studies in which we examine speedup, efficiency, total session time, and cost for sets of simulations of a published NEURON model.