18,688 AMD Opteron 6274 16-core CPUs
18,688 Nvidia Tesla K20 GPUs
17.59 petaflops
Titan displaced Sequoia (at Lawrence Livermore National Laboratory) from the top spot on Top500. Interestingly enough, Sequoia uses a very different architecture, based on 16-core PowerPC A2 nodes rather than GPUs. Sequoia also has about 1.6PB of memory, while Titan "only" has 1PB.
Both computers have reasonably different use cases. GPUs are great for embarrassingly parallel, non-memory intensive tasks like brute forcing passwords. But all of the rumors about the NSA's massive data analysis needs suggests that they may need a cluster that resembles Sequoia (with fewer cores, but larger caches and available memory) more than Titan.
So they could have easily fabbed something like this, or a tuned architecture specifically designed for the purpose.
Instead, they participate in a program to partner with domestic companies to manufacture their chips: http://trustedfoundryprogram.org/
considering that the entire purpose of NSA in the first place is to provide SIGINT and encrypt or decrypt signals, it's almost a given that they're trying to the best of their ability to crack stuff.
Money buys more commodity hardware faster than the time/money used to develop a chip
It's not hard to make tens, or maybe even hundreds of GPUs beat a specialized chip except for very specific things
And even for something specialized it's probably easier to use an FPGA
The combination is exotic enough to be considered non-commodity hardware.