In general, gRPC-go provides a concurrency-friendly API. What follows are some guidelines.
A ClientConn can safely be accessed concurrently. Using helloworld as an example, one could share the ClientConn across multiple goroutines to create multiple GreeterClient types. In this case, RPCs would be sent in parallel. GreeterClient, generated from the proto definitions and wrapping ClientConn, is also concurrency safe, and may be directly shared in the same way. Note that, as illustrated in the multiplex example, other Client types may share a single ClientConn as well.
When using streams, one must take care to avoid calling either SendMsg or RecvMsg multiple times against the same Stream from different goroutines. In other words, it's safe to have a goroutine calling SendMsg and another goroutine calling RecvMsg on the same stream at the same time. But it is not safe to call SendMsg on the same stream in different goroutines, or to call RecvMsg on the same stream in different goroutines.
Each RPC handler attached to a registered server will be invoked in its own goroutine. For example, SayHello will be invoked in its own goroutine. The same is true for service handlers for streaming RPCs, as seen in the route guide example here. Similar to clients, multiple services can be registered to the same server.