An introduction of intelligent interconnectivity for people and things has posed higher demands and more challenges for sixth-generation (6G) networks, such as high spectral efficiency and energy efficiency, ultra-low latency, and ultra-high reliability. Cell-free (CF) massive multiple-input multiple-output (mMIMO) and reconfigurable intelligent surface (RIS), also called intelligent reflecting surface (IRS), are two promising technologies for coping with these unprecedented demands. Given their distinct capabilities, integrating the two technologies to further enhance wireless network performances has received great research and development attention. In this paper, we provide a comprehensive survey of research on RIS-aided CF mMIMO wireless communication systems. We first introduce system models focusing on system architecture and application scenarios, channel models, and communication protocols. Subsequently, we summarize the relevant studies on system operation and resource allocation, providing in-depth analyses and discussions. Following this, we present practical challenges faced by RIS-aided CF mMIMO systems, particularly those introduced by RIS, such as hardware impairments and electromagnetic interference. We summarize corresponding analyses and solutions to further facilitate the implementation of RIS-aided CF mMIMO systems. Furthermore, we explore an interplay between RIS-aided CF mMIMO and other emerging 6G technologies, such as next-generation multiple-access (NGMA), simultaneous wireless information and power transfer (SWIPT), and millimeter wave (mmWave). Finally, we outline several research directions for future RIS-aided CF mMIMO systems.