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 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 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: migrate graphics processing from the local GPU to the virtual GPU; and execute an application using the virtual GPU.