There are three companies, including China Life Insurance, China Ping An, China Pacific, Second Corps, Xinhua Life Insurance, Taikang Life Insurance and Minsheng Life Insurance. There are many foreign-funded and joint-venture insurance companies with relatively small market share, and there are more than 30 newly-established companies, such as AIA, Haikang, Xincheng, Sino-British, Sino-American Metropolis, Zhong Yi, Hong Zhong, Jinsheng, Taiping, Life Insurance and PICC Life Insurance. AVIC Samsung, Pacific Antai, Haier New Yorker, Pioneer Antai, Hengkang Tianan, Optoelectronics Risheng, Huaxia, China Life Insurance, PICC Health Insurance, Kunlun Health Insurance, Ruifu Health Insurance, Huatai Life Insurance, Jiahe Life Insurance and Zhongxin Dadong can all be remembered. There are also Guohua Life Insurance and Xintai Life Insurance in preparation. That's all I know. I'm not sure which is better, but I'll know soon!
Further reading: How to buy insurance, which is good, and teach you how to avoid these "pits" of insurance.