seL4 is the big one: https://sel4.systems/

Here's a general reference of open source microkernel operating systems: http://www.microkernel.info/

Here's a general reference for open source real time operating systems: http://www.osrtos.com/

seL4 is really sexy, but I don't think it's anywhere near the most-used one?

OKL4 if we're going with the phone example. They stopped open-sourcing it by version 4.0 but someone should be able to dig up OKL4 3.0 somewhere.