1. A system, comprising: a virtual compute instance, wherein the virtual compute instance is implemented using central processing unit (CPU) resources and memory resources of a physical compute instance, wherein the virtual compute instance is provided by a multi-tenant provider network, and wherein the virtual compute instance is configured to execute an application; a physical graphics processing unit (GPU) accessible to the virtual compute instance over a network; one or more computing devices comprising one or more processors and memory and configured to implement an elastic graphics service providing virtual GPU services for a plurality of virtual GPU classes offering different graphics processing capabilities, wherein the elastic graphics service is configured to: attach a virtual GPU to the virtual compute instance, wherein the virtual GPU is selected from among the plurality of virtual GPU classes based at least in part on requirements for the application, and wherein the virtual GPU is implemented using the physical GPU; wherein the virtual compute instance is configured to: execute the application using the virtual GPU, wherein execution of the application generates output, and wherein the output is displayed on a display device associated with a client device.