XSEDE (formerly TeraGrid)
The Extreme Science and Engineering Discovery Environment is a group of large clusters and grids available free of charge for academic research.
Open Science Grid
The Open Science Grid is a very large scale global grid consisting of resources shared by numerous institutions.
Cornell Red Cloud
The Cornell Red Cloud is an on-demand research computing service available by subscription. It provides virtual servers managed by the subscriber, and a software service for running large-scale Matlab models utilizing the Matlab distributed computing server and nVidia GPUs.
There are many commercial services that provide virtual servers on a pay-as-you-go basis. For more information, please contact your facilitator.