Over the last century in the United States, the the number of tornadoes has been increasing while the death and injury rate has been dropping. This chart shows the last 100 years of tornadoes and their effects. The data is smoothed out using a ten year moving average to help show the overall trends.
It is clear that the number of injuries from tornadoes has plummeted. While this is most likely due to issues with the availability or reporting of data (see source), improved warning systems must be partly responsible, as we can see that the number of deaths has dropped dramatically over time (even in the face of increasingly active tornado seasons).
It is possible climate change has contributed to the upward-sloping trend from the 1990s on, meaning the number of tornadoes has increased due to the effects of global warming on weather systems. However, improved detection systems may also be at play. Modern satellite systems and avid tornado chasers ensure that every modern tornado is accounted for. If a tornado touched down in the middle of nowhere in 1925 and no one was around to witness or report it, it would not have been counted in the above data. In more recent years, meteorologists have had the technology available to detect tornadoes in rural and remote areas, thus accounting for some increase in the number of tornadoes on record.