I don't know about specific projects, but the main Ada use case I've heard about is safety-critical embedded systems in heavily regulated industries. The same sort of places you might use NASA JPL's famously strict rules for C code--things like control loops for jet engines. (One of the most compelling reasons to use Ada is SPARK, a theorem prover bolted onto the compiler that can formally verify your program doesn't violate any assertions or trigger any runtime errors.)

Nvidia, Boeing, many satellite programmes, Raven Ports http://www.ravenports.com/

One example would be the Boeing 777 flight control software.