Well, this was quick :-)
I don't have enough points to edit the wiki articles, so I guess I'll just toss a few here to get merged into the wiki articles:
math.NT: Cryptography (of course). A more quirky one is SETI (the primes in binary would be a very clear indication of a signal non-natural origin).
math.CA: Fourier analysis allows one to precisely divide up the electromagnetic spectrum, leading of course to radio, television, wireless, and so forth. MRI is based on inverting the Radon transform.
math.AP: Radar imaging is based on solving an inverse problem. The recent buzz about metamaterials and invisibility is based on understanding variable-coefficient elliptic problems.
math.RA: Google's Pagerank algorithm is based, in part, on the singular value decomposition.
math.CO: Group testing.
There's a way to use finite fields to multiplex cell phone signals so they don't interfere with each other, but the precise connection escapes me at present.