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 configured to implement an elastic graphics service, wherein the elastic graphics service is configured to: attach a virtual GPU to the virtual compute instance, wherein the virtual GPU is selected from a 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.