You can have your own argument about Uber's value as an industry-changing technology (just please don't torch anyone's car in the process). But one recent study looked at a particular effect of Uber: namely, when it started in California, did it reduce drinking and driving deaths?
The research was conducted by professors from Philidelphia's Temple University. They used data from the California Highway Patrol to examine the number of deaths due to alcohol-related car crashes, before and after UberX entered various cities.
The results suggest a small but strong correlation, with the entry of UberX into a city typically reducing the number of deaths by 3-5% in three months. The decrease in deaths is probably due to the cheapness of UberX: fares are around 20-30% cheaper than taxis, meaning drunk people are more likely to use UberX rather than driving home.
The number of deaths didn't budge when the more expensive UberBlack came to town, and also remains unchanged on weekends, when surge pricing typically comes into effect — in other words, it's all about the price.
The researcher's methodology seems reasonably robust — the dataset is collected independently, and the multiple cities and large sample size involved give a good degree of confidence to the results (although there's always room to be sceptical with this kind of statistical analysis).