Can ps display only non kernel processes on Linux?

This should do (under Linux):

ps --ppid 2 -p 2 --deselect

kthreadd (PID 2) has PPID 0 (on Linux 2.6+) but ps does not allow to filter for PPID 0; thus this work-around.

One way to recognize kernel processes is that they don't use any user memory, so the vsz field is 0. This also catches zombies (thanks to Stephane Chazelas for this observation), which can be eliminated based on their status.

ps axl | awk '$7 != 0 && $10 !~ "Z"'

To list just the PIDs:

ps -e -o pid= -o state= -o vsize= | awk '$2 != "Z" && $3 != 0 {print $1}'

In practice I found the following idiom enough:

ps auxf | grep -v ]$

It filters lines ending with brackets, which might result omitting unwanted entries but it's very unlikely. In exchange it's quite easy to remember and relatively quick to type.

Some processes like avahi-daemon add to their process name information in brackets (the hostname in the case of avahi-daemon) and will be filtered out by this command.