Data access patterns that involve fine-grained sharing, multicasts, or reductions have proved to be hard to scale in sharedmemory platforms. Recently, wireless on-chip communication has been proposed as a solution to this problem, but a previous architecture has used it only to speed-up synchronization. An intriguing question is whether wireless communication can be widely effective for ordinary shared data. This paper presents Replica, a manycore that uses wireless communication for communication-intensive ordinary data. To deliver high performance, Replica supports an adaptive wireless protocol and selective message dropping. We describe the computational patterns that leverage wireless communication, programming techniques to restructure applications, and tools that help with automation. Our results show that wireless communication is effective for ordinary data. For 64 cores, Replica obtains a mean speed-up of 1.76x over a conventional machine. The mean speed-up reaches 1.89x if approximate-computing transformations are enabled. The average energy consumption is substantially reduced by 34% (or 38% with approximate transformations), and the area increases only modestly.