Earthquake prediction has been a long-term debatable problem in earthquake science. There were numerous studies of possible precursors after the M_w 7.6 Chi-Chi, Taiwan, earthquake of 20 September 1999. A deep study about these precursors will be useful for the exploration of the debatable problem. In this study, based on the time window (or the precursor time, T) prediction for earthquakes in Taiwan are defined as follows: very-long-term prediction (T > ten years or longer); long-term prediction (ten years> T > three years); intermediate-term prediction (T = six months to three years); short-term prediction (T = eight days to six months); and imminent prediction (T ≤ seven days). Meanwhile, the precursors are classified into four categories: mechanical, electromagnetic, geochemical, and biological precursors. Each category may include several items. First, we will compile all given possible precursors and the respective precursor times. Secondly, we will examine these possible precursors based on known physical and chemical theories. Thirdly, we will discuss the possible correlations between two precursors. From the results of this study, most of precursors are reliable and few of them need re-examinations. This suggests the possibility of earthquake prediction. Nevertheless, earthquake scientists cannot yet preciously predict an earthquake just based on the reliable observations. Like weather forecasting, it is very necessary to construct the physical and chemical models of respective precursors or even a unified model for all precursors. Based on the models or a unified model, it is possible to predict earthquakes.