We make use of the extant testing methodology of Barndorff-Nielsen and Shephard (2006) and Aït-Sahalia and Jacod (2009a,b,c) to examine the importance of jumps, and in particular large and small jumps, using high frequency price returns on 25 stocks in the DOW 30 and S&P futures index. In particular, we examine jumps from both the perspective of their contribution to overall realized variation and their contribution to predictive regressions of realized volatility. We find evidence of jumps in around 22.8% of the days during the 1993-2000 period, and in 9.4% of the days during the 2001-2008 period, which implies more (jump induced) turbulence in financial markets in the previous decade than the current decade. Also, it appears that frequent small jumps of the 1990s have been replaced to some extent with relatively infrequent large jumps in recent years. Interestingly, this result holds for all of the stocks that we examine, supporting the notion that there is strong comovement across jump components for a wide variety of stocks, as discussed in Bollerslev, Law and Tauchen (2008). In our prediction experiments using the class of linear and nonlinear HAR-RV, HAR-RV-J and HAR-RV-CJ models proposed by Müller, Dacorogna, Davé, Olsen, Puctet, and von Weizsäckeret (1997), Corsi (2004) and Andersen, Bollerslev and Diebold (2007). we find that the linear model performs well for only very few stocks, while there is significant improvement when instead using the square root model. Interestingly, the log model, which performs very well in their study of market indices, performs approximately equally as well as the square root model when our longer sample of market index data is used. Moreover, the log model, while yielding marked predictability improvements for individual stocks, can actually only be implemented for 7 of our 25 stocks, due to data singularity issues associated with the incidence of jumps at the level of individual stocks.