Long memory has always played a central role in physics since it was first discovered by Hurst while studying the flow of the River Nile. Interestingly, after his seminal work, many other researchers found the same pattern in other domains of science, such as biology, economics and finance. These studies have mainly relied on the use of the Hurst exponents as a measure of the degree of memory in a process. In this paper we use a different approach based on the FIGARCH (fractional integrated generalized autoregressive conditionally heteroskedasticity) model proposed by Baillie et al. in order to analyze the long memory behavior of stock market volatility. More specifically, we compare how the long memory parameter evolves before and after the 2008 and 2012 crises in both developed and emerging markets. Specifically, we consider the daily returns of the S&P 500, STOXX 50, FTSE 100, NIKKEI 225, HSI, BUX, WIG, SSE, IDX and KLCI indices for the period from October 1, 2003 to October 2, 2015 and then split the whole sample into four sub-samples of roughly three years each. Results show different patterns for the pre and post crisis periods revealing that the degree of memory differs in accordance with the country's development and the level of market turbulence. In particular, we found that major mature economies present higher levels of long memory than emerging countries and were more affected by the 2008 and 2012 crises.