In recent years, cloud computing has become a new trend of Internet applications and can potentially bring benefits and new business models for various industries and applications. In this paper, we first review two traditional Internet-based remote monitoring and control (RMC) architectures, i.e. AVMS (Automatic Virtual Metrology System) for equipment monitoring and ZDPMCS (ZigBee-based Distributed Power Monitoring and Control System) for power monitoring. Then, their corresponding new architectures based on cloud computing are developed. Specifically, a cloud-computing-based intelligent equipment monitoring architecture (CCIEMA) is proposed. The CCIEMA mainly consists of three parts: cloud side-providing various equipment monitoring related cloud services, equipment side-containing several equipment managers for monitoring and controlling equipment, and client side-including various Web-based GUIs for users to interact with the system. Based on the proposed CCIEMA, various prediction models can be created on the cloud and then downloaded to the equipment manager for performing yield rate prediction, machining precision conjecture, and remaining useful life prediction. By the same approach, we also propose a new power monitoring and control architecture based on cloud computing and ZigBee, called CZPMCA, and show its major operational scenarios. The potential benifits of the proposed CCIEMA and CZPMCA are described as well, compared to the tradiotional RMC architectures. The research results can be useful references for constructing various RMC systems using cloud computing.