Cloud storage systems generally add redundancy in storing content files such that $K$ files are replicated or erasure coded and stored on $N > K$ nodes. In addition to providing reliability against failures, the redundant copies can be used to serve a larger volume of content access requests. A request for one of the files can be either be sent to a systematic node, or one of the repair groups. In this paper, we seek to maximize the service capacity region, that is, the set of request arrival rates for the $K$ files that can be supported by a coded storage system. We explore two aspects of this problem: 1) for a given erasure code, how to optimally split incoming requests between systematic nodes and repair groups, and 2) choosing an underlying erasure code that maximizes the achievable service capacity region. In particular, we consider MDS and Simplex codes. Our analysis demonstrates that erasure coding makes the system more robust to skews in file popularity than simply replicating a file at multiple servers, and that coding and replication together can make the capacity region larger than either alone.