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 comprises a local graphics processing unit (GPU), and wherein the virtual compute instance is provided by a multi-tenant provider network; a physical GPU accessible to the virtual compute instance over a network; one or more computing devices comprising one or more processors and a memory, the memory storing instructions that, when executed on the one or more processors, cause the one or more processors 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 provides improved graphics processing relative to the local GPU, wherein the virtual GPU is selected from a plurality of virtual GPU classes based at least in part on computational or memory resources, and wherein the virtual GPU is implemented using the physical GPU; wherein the virtual compute instance is configured to: initiate execution of an application using the local GPU; migrate graphics processing from the local GPU to the virtual GPU during execution of the application; and execute the application using the virtual GPU.