This study examines the random walk hypothesis and the weak-form efficiency of fifteen stock markets in lower-middle income, upper-middle income and high-income economies across the world. Statistical tests including the Jacque-Bera test, the Augmented Dickey-Fuller test, the runs test, the autocorrelation test and the variance ratio test are applied to weekly returns series of a major market index of each of the fifteen (15) stock markets collected over the period of January 2, 2011, to December 31, 2019. This study documents evidence that the stock markets of Australia, Chile, Germany, Norway, the United States of America, Argentina, Brazil, China, Russia, Egypt, India, Indonesia and the Republic of South Africa are weak-form efficient even though their return series do not follow a random walk. It is, however, found that the stock markets of Ghana and Mexico are not weak-form efficient. These findings imply that stock prices of the weak-form efficient markets fully reflect past price information and that investors cannot formulate investment strategies based on past price information in order to earn above-average returns. Conversely, the results on the Ghanaian and Mexican stock markets signify that stock prices of are predicable so there is a possibility for investors to exploit this market inefficiency.