The stated defense for the practices of the NSA is the need to proactively seek out terrorist threats in the modern era of asymmetric warfare. Ignoring the complexities of a cost-benefit analysis of Privacy vs Safety, is there any evidence to the success of these practices more so than standard watchlist/warrant searches?
According to Gen. Keith Alexander, the information collected by the PRISM program has been a part stopping "over 50" terrorist plots as of 2013. During a House Intelligence Committee hearing, the ex-NSA director called out three specific cases where PRISM played a role: the case of Najibullah Zazi and Adis Medunjanin, Khalid Ouazzani, and David Headley.
Since PRISM is administered by the NSA and Gen. Alexander was instrumental in it's implementation, his personal perspective on its effectiveness should be kept in mind. A University of Tennessee student wrote a thesis from the opposite perspective: Mass Surveillance and Terrorism: Does PRISM Keep Americans Safer? The author there highlights the use of traditional surveillance methods for intelligence gathering and their success, and Edward Snowden argued after Alexander's testimony that the use of PRISM wasn't necessary in the cases they mentioned:
It has been argued by Snowden and others that the coded email message that foiled Zazi's plot could have been uncovered without the controversial PRISM electronic surveillance program, which apparently collects data from everyone for later dissection and not just suspected terrorists.
So the ultimate answer in my mind is: it depends. It depends on how much you trust or distrust the officials at the NSA that say that it has, and it depends on how much importance someone places on a specific piece of information uncovered by PRISM when it comes to any individual case. Surely, even in those cases the NSA highlighted in congressional testimony, there was traditional surveillence and intelligence gathering taking place, and how important PRISM is in any single case specifically is a bit of a judgement call. We unfortunately don't have access to all of the information required to make an informed decision.