There are a lot of reasons to believe that volatility has gotten more severe in modern markets. This week alone the S&P 500 lost 40 points Monday and Tuesday and then gained 30 points between Wednesday and today (assuming we close around here). Many will blame algorithmic trading and increased information flow for this volatility, but really the most likely culprit is human emotion, which hasn't actually changed much for the last 100 years.
The chart below is a chart of the volatility of the Dow going back for 100 years. The volatility is measured as the percentage change intra-quarter from the low point of the quarter to the high point of the quarter. There are periods of high volatility but overall, the average volatility has been fairly constant over this period.
The argument could be made that there is a slight structural increase in volatility from about 10% per quarter in the 50s and 60s to about 14% per quarter in the 90s-00s. However, this doesn't explain the fact that the depression period registered the highest period of volatility despite a lack of algorithms and internet.