Many antennas are designed for a given gain and polarization, and you get the impedance you get from the materials and geometry used. Almost all of them have a matching network at the entrance to the antenna, and usually one set up based on actual S-parameter measurements. If you're really fancy, you can get custom coax cables made to match your antenna at any arbitrary impedance, and then put a much better matching circuit in your rack instead of using one on the antenna.
High-speed digital signals haven't entirely settled on 50 ohm (100 ohm differential) impedance, though. SSTL, HSTL, and POD (used by different types of memory and high-speed DACs/ADCs) often use 35-40 ohm impedance instead of 50. It's also not uncommon to see drivers having lower impedance and receivers having higher impedance (eg having a 32 ohm driver and a 48 ohm receiver on a 40 ohm wire) because a little bit of reflection can actually help signal integrity here.
Long digital wires like twinax Ethernet are all 100 ohm differential signals, though, since reflection is not beneficial there at all.