Which process has PID 0?

From the wikipedia page titled: Process identifier:

There are two tasks with specially distinguished process IDs: swapper or sched has process ID 0 and is responsible for paging, and is actually part of the kernel rather than a normal user-mode process. Process ID 1 is usually the init process primarily responsible for starting and shutting down the system. Originally, process ID 1 was not specifically reserved for init by any technical measures: it simply had this ID as a natural consequence of being the first process invoked by the kernel. More recent Unix systems typically have additional kernel components visible as 'processes', in which case PID 1 is actively reserved for the init process to maintain consistency with older systems.

You can see the evidence of this if you look at the parent PIDs (PPID) of init and kthreadd:

$ ps -eaf
UID        PID  PPID  C STIME TTY          TIME CMD
root         1     0  0 Jun24 ?        00:00:02 /sbin/init
root         2     0  0 Jun24 ?        00:00:00 [kthreadd]

kthreadd is the kernel thread daemon. All kthreads are forked from this thread. You can see evidence of this if you look at other processes using ps and seeing who their PPID is:

$ ps -eaf
root         3     2  0 Jun24 ?        00:00:57 [ksoftirqd/0]
root         4     2  0 Jun24 ?        00:01:19 [migration/0]
root         5     2  0 Jun24 ?        00:00:00 [watchdog/0]
root        15     2  0 Jun24 ?        00:01:28 [events/0]
root        19     2  0 Jun24 ?        00:00:00 [cpuset]
root        20     2  0 Jun24 ?        00:00:00 [khelper]

Notice they're all 2.

From Process Identifier wiki:

There are two tasks with specially distinguished process IDs: swapper or sched has process ID 0 and is responsible for paging, and is actually part of the kernel rather than a normal user-mode process.

The process with pid 0 is the scheduler,

Process ID Description:
0 The Scheduler
1 The init process
2 kflushd
3 kupdate
4 kpiod
5 kswapd
6 mdrecoveryd