With the proliferation of multimedia content on the Internet, there is an increasing demand for video streams with high perceptual quality. The capability of present-day Internet links in delivering high-perceptual-quality streaming services, however, is not completely understood. Link-level degradations caused by intradomain routing policies and inter-ISP peering policies are hard to obtain, as Internet service providers often consider such information proprietary. Understanding link-level degradations will enable us in designing future protocols, policies, and architectures to meet the rising multimedia demands. This paper presents a trace-driven study to understand quality-of-experience (QoE) capabilities of present-day Internet links using 51 diverse ISPs with a major presence in the US, Europe, and Asia-Pacific. We study their links from 38 vantage points in the Internet using both passive tracing and active probing for six days. We provide the first measurements of link-level degradations and case studies of intra-ISP and inter-ISP peering links from a multimedia standpoint. Our study offers surprising insights into intradomain traffic engineering, peering link loading, BGP, and the inefficiencies of using autonomous system (AS)-path lengths as a routing metric. Though our results indicate that Internet routing policies are not optimized for delivering high-perceptual-quality streaming services, we argue that alternative strategies such as overlay networks can help meet QoE demands over the Internet. Streaming services apart, our Internet measurement results can be used as an input to a variety of research problems.